Annals of Functional Analysis Articles (Project Euclid)
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The latest articles from Annals of Functional Analysis on Project Euclid, a site for mathematics and statistics resources.en-usCopyright 2014 Cornell University LibraryEuclid-L@cornell.edu (Project Euclid Team)Thu, 06 Feb 2014 16:40 ESTThu, 06 Feb 2014 16:40 ESThttp://projecteuclid.org/collection/euclid/images/logo_linking_100.gifProject Euclid
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Hölder type inequalities on Hilbert $C^*$-modules and its reverses
http://projecteuclid.org/euclid.afa/1391614563
<strong>Yuki Seo</strong>. <p><strong>Source: </strong>Annals of Functional Analysis, Volume 5, Number 1, 1--9.</p><p><strong>Abstract:</strong><br/>
In this paper, we show Hilbert $C^*$-module versions of Hölder--McCarthy
inequality and its complementary inequality. As an application, we obtain
Hölder type inequalities and its reverses on a Hilbert $C^*$-module.
</p>projecteuclid.org/euclid.afa/1391614563_20140206164041Thu, 06 Feb 2014 16:40 ESTBases in some spaces of Whitney functionshttps://projecteuclid.org/euclid.afa/1498723216<strong>Alexander Goncharov</strong>, <strong>Zeliha Ural</strong>. <p><strong>Source: </strong>Annals of Functional Analysis, Advance publication, 16 pages.</p><p><strong>Abstract:</strong><br/>
We construct topological bases in spaces of Whitney functions on Cantor sets, which were introduced by the first author. By means of suitable individual extensions of basis elements, we construct a linear continuous extension operator, when it exists for the corresponding space. In general, elements of the basis are restrictions of polynomials to certain subsets. In the case of small sets, we can present strict polynomial bases as well.
</p>projecteuclid.org/euclid.afa/1498723216_20180104220516Thu, 04 Jan 2018 22:05 ESTA treatment of strongly operator-convex functions that does not require any knowledge of operator algebrashttps://projecteuclid.org/euclid.afa/1498723217<strong>Lawrence G. Brown</strong>. <p><strong>Source: </strong>Annals of Functional Analysis, Advance publication, 15 pages.</p><p><strong>Abstract:</strong><br/>
In a previous article, we proved the equivalence of six conditions on a continuous function $f$ on an interval. These conditions determine a subset of the set of operator-convex functions whose elements are called strongly operator-convex . Two of the six conditions involve operator-algebraic semicontinuity theory, as given by Akemann and Pedersen, and the other four conditions do not involve operator algebras at all. Two of these conditions are operator inequalities, one is a global condition on $f$ , and the fourth is an integral representation of $f$ , stronger than the usual integral representation for operator-convex functions. The purpose of this article is to make the equivalence of these four conditions accessible to people who do not know operator algebra theory as well as to operator algebraists who do not know the semicontinuity theory. A treatment of other operator inequalities characterizing strong operator convexity is included.
</p>projecteuclid.org/euclid.afa/1498723217_20180104220516Thu, 04 Jan 2018 22:05 ESTConvergence properties of nets of operatorshttps://projecteuclid.org/euclid.afa/1498723218<strong>Fadel Nasaireh</strong>, <strong>Dorian Popa</strong>, <strong>Ioan Rasa</strong>. <p><strong>Source: </strong>Annals of Functional Analysis, Advance publication, 7 pages.</p><p><strong>Abstract:</strong><br/>
We consider nets $(T_{j})$ of operators acting on complex functions, and we investigate the algebraic and the topological structure of the set $\{f:T_{j}(|f|^{2})-|T_{j}f|^{2}\rightarrow 0\}$ . Our results extend and improve some known results from the literature, which are connected with Korovkin’s theorem. Applications to Abel–Poisson-type operators and Bernstein-type operators are given.
</p>projecteuclid.org/euclid.afa/1498723218_20180104220516Thu, 04 Jan 2018 22:05 ESTNonexpansive bijections between unit balls of Banach spaceshttps://projecteuclid.org/euclid.afa/1515812424<strong>Olesia Zavarzina</strong>. <p><strong>Source: </strong>Annals of Functional Analysis, Advance publication, 11 pages.</p><p><strong>Abstract:</strong><br/>
It is known that if $M$ is a finite-dimensional Banach space, or a strictly convex space, or the space $\ell_{1}$ , then every nonexpansive bijection $F\colon B_{M}\to B_{M}$ of its unit ball $B_{M}$ is an isometry. We extend these results to nonexpansive bijections $F\colon B_{E}\to B_{M}$ between unit balls of two different Banach spaces. Namely, if $E$ is an arbitrary Banach space and $M$ is finite-dimensional or strictly convex, or the space $\ell_{1}$ , then every nonexpansive bijection $F\colon B_{E}\to B_{M}$ is an isometry.
</p>projecteuclid.org/euclid.afa/1515812424_20180112220049Fri, 12 Jan 2018 22:00 ESTA note on the hypercyclicity of operator-weighted shiftshttps://projecteuclid.org/euclid.afa/1517216425<strong>Ya Wang</strong>, <strong>Ze-Hua Zhou</strong>. <p><strong>Source: </strong>Annals of Functional Analysis, Advance publication, 12 pages.</p><p><strong>Abstract:</strong><br/>
In this article, we give equivalent conditions for the hypercyclicity of bilateral operator-weighted shifts on $L^{2}(\mathcal{K})$ with weight sequence $\{A_{n}\}_{n=-\infty}^{\infty}$ of positive invertible diagonal operators on a separable complex Hilbert space $\mathcal{K}$ , as well as for hereditarily hypercyclicity and supercyclicity.
</p>projecteuclid.org/euclid.afa/1517216425_20180129040120Mon, 29 Jan 2018 04:01 ESTTensor products of hyperrigid operator systemshttps://projecteuclid.org/euclid.afa/1520046333<strong>P. Shankar</strong>, <strong>A. K. Vijayarajan</strong>. <p><strong>Source: </strong>Annals of Functional Analysis, Volume 9, Number 3, 369--375.</p><p><strong>Abstract:</strong><br/>
In this article, we prove that the tensor product of two hyperrigid operator systems is hyperrigid in the spatial tensor product of $C^{*}$ -algebras. We deduce this by establishing that the unique extension property for unital completely positive maps on operator systems carry over to tensor products such maps defined on the tensor product operator systems. Hopenwasser’s result about the tensor product of boundary representations follows as a special case. We also provide examples to illustrate the hyperrigidity property of tensor products of operator systems.
</p>projecteuclid.org/euclid.afa/1520046333_20180809220627Thu, 09 Aug 2018 22:06 EDTOn multipliers between bounded variation spaceshttps://projecteuclid.org/euclid.afa/1517886230<strong>Héctor Camilo Chaparro</strong>. <p><strong>Source: </strong>Annals of Functional Analysis, Volume 9, Number 3, 376--383.</p><p><strong>Abstract:</strong><br/>
Wiener-type variation spaces, also known as $\operatorname{BV}_{p}$ -spaces ( $1\leq p\lt \infty$ ), are complete normed linear spaces. A function $g$ is called a multiplier from $\operatorname{BV}_{p}$ to $\operatorname{BV}_{q}$ if the pointwise multiplication $fg$ belongs to $\operatorname{BV}_{q}$ for each $f\in\operatorname{BV}_{p}$ . In this article, we characterize the multipliers from $\operatorname{BV}_{p}$ to $\operatorname{BV}_{q}$ for the cases $1\leq q\lt p$ and $1\leq p\leq q$ .
</p>projecteuclid.org/euclid.afa/1517886230_20180809220627Thu, 09 Aug 2018 22:06 EDTHausdorff operators on modulation and Wiener amalgam spaceshttps://projecteuclid.org/euclid.afa/1517886229<strong>Guoping Zhao</strong>, <strong>Dashan Fan</strong>, <strong>Weichao Guo</strong>. <p><strong>Source: </strong>Annals of Functional Analysis, Volume 9, Number 3, 398--412.</p><p><strong>Abstract:</strong><br/>
We give sharp conditions for boundedness of Hausdorff operators on certain modulation and Wiener amalgam spaces.
</p>projecteuclid.org/euclid.afa/1517886229_20180809220627Thu, 09 Aug 2018 22:06 EDTNonlinear harmonic analysis of integral operators in weighted grand Lebesgue spaces and applicationshttps://projecteuclid.org/euclid.afa/1517886227<strong>Alberto Fiorenza</strong>, <strong>Vakhtang Kokilashvili</strong>. <p><strong>Source: </strong>Annals of Functional Analysis, Volume 9, Number 3, 413--425.</p><p><strong>Abstract:</strong><br/>
In this article, we give a boundedness criterion for Cauchy singular integral operators in generalized weighted grand Lebesgue spaces. We establish a necessary and sufficient condition for the couple of weights and curves ensuring boundedness of integral operators generated by the Cauchy singular integral defined on a rectifiable curve. We characterize both weak and strong type weighted inequalities. Similar problems for Calderón–Zygmund singular integrals defined on measured quasimetric space and for maximal functions defined on curves are treated. Finally, as an application, we establish existence and uniqueness, and we exhibit the explicit solution to a boundary value problem for analytic functions in the class of Cauchy-type integrals with densities in weighted grand Lebesgue spaces.
</p>projecteuclid.org/euclid.afa/1517886227_20180809220627Thu, 09 Aug 2018 22:06 EDTThe perturbation class of algebraic operators and applicationshttps://projecteuclid.org/euclid.afa/1517886228<strong>Mourad Oudghiri</strong>, <strong>Khalid Souilah</strong>. <p><strong>Source: </strong>Annals of Functional Analysis, Volume 9, Number 3, 426--434.</p><p><strong>Abstract:</strong><br/>
In this article, we completely describe the perturbation class, the commuting perturbation class, and the topological interior of the class of all bounded linear algebraic operators. As applications, we also focus on the stability of the essential ascent spectrum and the essential descent spectrum under finite-rank perturbations.
</p>projecteuclid.org/euclid.afa/1517886228_20180809220627Thu, 09 Aug 2018 22:06 EDTPerturbation analysis for the (skew) Hermitian matrix least squares problem $AXA^{H}=B$https://projecteuclid.org/euclid.afa/1524038416<strong>Si-Tao Ling</strong>, <strong>Rui-Rui Wang</strong>, <strong>Qing-Bing Liu</strong>. <p><strong>Source: </strong>Annals of Functional Analysis, Volume 9, Number 4, 435--450.</p><p><strong>Abstract:</strong><br/>
In this article, we study the perturbation analysis for the (skew) Hermitian matrix least squares problem (LSP). Suppose that $\mathcal{S}$ and $\widehat{\mathcal{S}}$ are two sets of solutions to the (skew) Hermitian matrix least squares problem $AXA^{H}=B$ and the perturbed Hermitian matrix least squares problem $\widehat{A}\widehat{X}\widehat{A}^{H}=\widehat{B}$ , respectively. For any given $X\in\mathcal{S}$ , we derive general expressions of the least squares solutions $\widehat{X}\in\widehat{\mathcal{S}}$ that are closest to $X$ , and we present the corresponding distances between them under appropriate norms. Perturbation bounds for the nearest least squares solutions are further derived.
</p>projecteuclid.org/euclid.afa/1524038416_20181102220101Fri, 02 Nov 2018 22:01 EDTA note on stability of Hardy inequalitieshttps://projecteuclid.org/euclid.afa/1529028135<strong>Michael Ruzhansky</strong>, <strong>Durvudkhan Suragan</strong>. <p><strong>Source: </strong>Annals of Functional Analysis, Volume 9, Number 4, 451--462.</p><p><strong>Abstract:</strong><br/>
In this note, we formulate recent stability results for Hardy inequalities in the language of Folland and Stein’s homogeneous groups. Consequently, we obtain remainder estimates for Rellich-type inequalities on homogeneous groups. Main differences from the Euclidean results are that the obtained stability estimates hold for any homogeneous quasinorm.
</p>projecteuclid.org/euclid.afa/1529028135_20181102220101Fri, 02 Nov 2018 22:01 EDTA note on the $C$ -numerical radius and the $\lambda$ -Aluthge transform in finite factorshttps://projecteuclid.org/euclid.afa/1524470416<strong>Xiaoyan Zhou</strong>, <strong>Junsheng Fang</strong>, <strong>Shilin Wen</strong>. <p><strong>Source: </strong>Annals of Functional Analysis, Volume 9, Number 4, 463--473.</p><p><strong>Abstract:</strong><br/>
We prove that for any two elements $A$ , $B$ in a factor ${\mathcal{M}}$ , if $B$ commutes with all the unitary conjugates of $A$ , then either $A$ or $B$ is in $\mathbb{C}I$ . Then we obtain an equivalent condition for the situation that the $C$ -numerical radius $\omega_{C}(\cdot)$ is a weakly unitarily invariant norm on finite factors, and we also prove some inequalities on the $C$ -numerical radius on finite factors. As an application, we show that for an invertible operator $T$ in a finite factor ${\mathcal{M}}$ , $f(\bigtriangleup_{\lambda}(T))$ is in the weak operator closure of the set $\{\sum_{i=1}^{n}z_{i}U_{i}f(T)U_{i}^{*}\mid n\in\mathbb{N},(U_{i})_{1\leq i\leq n}\in\mathscr{U}({\mathcal{M}}),\sum_{i=1}^{n}\vert z_{i}\vert \leq1\}$ , where $f$ is a polynomial, $\bigtriangleup_{\lambda}(T)$ is the $\lambda$ -Aluthge transform of $T$ , and $0\leq\lambda\leq1$ .
</p>projecteuclid.org/euclid.afa/1524470416_20181102220101Fri, 02 Nov 2018 22:01 EDTOn pseudospectral radii of operators on Hilbert spaceshttps://projecteuclid.org/euclid.afa/1527213855<strong>Boting Jia</strong>, <strong>Youling Feng</strong>. <p><strong>Source: </strong>Annals of Functional Analysis, Volume 9, Number 4, 474--484.</p><p><strong>Abstract:</strong><br/>
For $\varepsilon\gt 0$ and a bounded linear operator $T$ acting on some Hilbert space, the $\varepsilon$ -pseudospectrum of $T$ is $\sigma_{\varepsilon}(T)=\{z\in\mathbb{C}:\|(zI-T)^{-1}\|\gt 1/\varepsilon\}$ and the $\varepsilon$ -pseudospectral radius of $T$ is $r_{\varepsilon}(T)=\sup\{|z|:z\in\sigma_{\varepsilon}(T)\}$ . In this article, we provide a characterization of those operators $T$ satisfying $r_{\varepsilon}(T)=r(T)+\varepsilon$ for all $\varepsilon\gt 0$ . Here $r(T)$ denotes the spectral radius of $T$ .
</p>projecteuclid.org/euclid.afa/1527213855_20181102220101Fri, 02 Nov 2018 22:01 EDTOn a lifting question of Blackadarhttps://projecteuclid.org/euclid.afa/1525420814<strong>Yuanhang Zhang</strong>. <p><strong>Source: </strong>Annals of Functional Analysis, Volume 9, Number 4, 485--499.</p><p><strong>Abstract:</strong><br/>
Let $A$ be the AF algebra whose scaled ordered group $K_{0}(A)$ is $(G\oplus H,(G_{+}\setminus\{0\})\oplus H\cup\{(0,0)\},\tilde{g}\oplus0)$ , where $(G,G_{+},\tilde{g})$ is the scaled ordered group $K_{0}(B)$ of a unital simple AF algebra $B$ , and $H$ is a countable torsion-free Abelian group. Let $\sigma$ be an order 2 scaled ordered automorphism of $K_{0}(A)$ , defined by $\sigma(g,h)=(g,-h)$ , where $(g,h)\in G\oplus H$ . We show that there is an order $2$ automorphism $\alpha$ of $A$ such that $\alpha_{*}=\sigma$ . This gives a partial answer to a lifting question posed by Blackadar. Incidentally, the lift $\alpha$ we construct has the tracial Rokhlin property. Consequently, the crossed product $C^{*}(\mathbb{Z}_{2},A,\alpha)$ is a unital simple AH algebra with no dimension growth.
</p>projecteuclid.org/euclid.afa/1525420814_20181102220101Fri, 02 Nov 2018 22:01 EDTNuclearity and trace formulas of integral operatorshttps://projecteuclid.org/euclid.afa/1525420816<strong>José Claudinei Ferreira</strong>, <strong>Suélen Almeida Carvalho</strong>. <p><strong>Source: </strong>Annals of Functional Analysis, Volume 9, Number 4, 500--513.</p><p><strong>Abstract:</strong><br/>
We present some results on the nuclearity (or trace class) of integral operators acting on $L^{2}(X,\nu)$ under specific conditions. These results improve and adapt a number of methods found in references on this subject. Our discussions take place within the context of special subsets (and manifolds) of the Euclidean space (endowed with weighted Lebesgue measure), second-countable spaces, and Lusin and Souslin spaces (endowed with $\sigma$ -finite Borel measure).
</p>projecteuclid.org/euclid.afa/1525420816_20181102220101Fri, 02 Nov 2018 22:01 EDTOperator approximate biprojectivity of locally compact quantum groupshttps://projecteuclid.org/euclid.afa/1525420815<strong>Mohammad Reza Ghanei</strong>, <strong>Mehdi Nemati</strong>. <p><strong>Source: </strong>Annals of Functional Analysis, Volume 9, Number 4, 514--524.</p><p><strong>Abstract:</strong><br/>
We initiate a study of operator approximate biprojectivity for quantum group algebra $L^{1}({\Bbb{G}})$ , where $\mathbb{G}$ is a locally compact quantum group. We show that if $L^{1}({\Bbb{G}})$ is operator approximately biprojective, then $\mathbb{G}$ is compact. We prove that if $\mathbb{G}$ is a compact quantum group and $\mathbb{H}$ is a non-Kac-type compact quantum group such that both $L^{1}({\Bbb{G}})$ and $L^{1}({\Bbb{H}})$ are operator approximately biprojective, then $L^{1}({\Bbb{G}})\widehat{\otimes}L^{1}({\Bbb{H}})$ is operator approximately biprojective, but not operator biprojective.
</p>projecteuclid.org/euclid.afa/1525420815_20181102220101Fri, 02 Nov 2018 22:01 EDTA new approach to the nonsingular cubic binary moment problemhttps://projecteuclid.org/euclid.afa/1529028136<strong>Raúl E. Curto</strong>, <strong>Seonguk Yoo</strong>. <p><strong>Source: </strong>Annals of Functional Analysis, Volume 9, Number 4, 525--536.</p><p><strong>Abstract:</strong><br/>
We present an alternative solution to nonsingular cubic moment problems, using techniques that are expected to be useful for higher-degree truncated moment problems. In particular, we apply the theory of recursively determinate moment matrices to deal with a case of rank-increasing moment matrix extensions.
</p>projecteuclid.org/euclid.afa/1529028136_20181102220101Fri, 02 Nov 2018 22:01 EDTCarleson measures for the generalized Schrödinger operatorhttps://projecteuclid.org/euclid.afa/1531361006<strong>S. Qi</strong>, <strong>Y. Liu</strong>, <strong>Y. Zhang</strong>. <p><strong>Source: </strong>Annals of Functional Analysis, Volume 9, Number 4, 537--550.</p><p><strong>Abstract:</strong><br/>
Let $\mathcal{L}=-\Delta+\mu$ be the generalized Schrödinger operator on $\mathbb{R}^{n}$ , $n\geq3$ , where $\Delta$ is the Laplacian and $\mu\nequiv0$ is a nonnegative Radon measure on $\mathbb{R}^{n}$ . In this article, we give a characterization of $\mathrm{BMO}_{\mathcal{L}}$ in terms of Carleson measures, where $\mathrm{BMO}_{\mathcal{L}}$ is the $\mathrm{BMO}$ -type space associated with the generalized Schrödinger operator.
</p>projecteuclid.org/euclid.afa/1531361006_20181102220101Fri, 02 Nov 2018 22:01 EDTApproximate amenability and contractibility of hypergroup algebrashttps://projecteuclid.org/euclid.afa/1539137305<strong>J. Laali</strong>, <strong>R. Ramezani</strong>. <p><strong>Source: </strong>Annals of Functional Analysis, Volume 9, Number 4, 551--565.</p><p><strong>Abstract:</strong><br/>
Let $K$ be a hypergroup. The purpose of this article is to study the notions of amenability of the hypergroup algebras $L(K)$ , $M(K)$ , and $L(K)^{**}$ . Among other results, we obtain a characterization of approximate amenability of $L(K)^{**}$ . Moreover, we introduce the Banach space $L_{\infty}(K,L(K))$ and prove that the dual of a Banach hypergroup algebra $L(K)$ can be identified with $L_{\infty}(K,L(K))$ . In particular, $L(K)$ is an $F$ -algebra. By using this fact, we give necessary and sufficient conditions for $K$ to be left-amenable.
</p>projecteuclid.org/euclid.afa/1539137305_20181102220101Fri, 02 Nov 2018 22:01 EDTGeneralizations of Jensen’s operator inequality for convex functions to normal operatorshttps://projecteuclid.org/euclid.afa/1538121758<strong>László Horváth</strong>. <p><strong>Source: </strong>Annals of Functional Analysis, Volume 9, Number 4, 566--573.</p><p><strong>Abstract:</strong><br/>
In this article, we generalize a well-known operator version of Jensen’s inequality to normal operators. The main techniques employed here are the spectral theory for bounded normal operators on a Hilbert space, and different Jensen-type inequalities. We emphasize the application of a vector version of Jensen’s inequality. By applying our results, some classical inequalities obtained for self-adjoint operators can also be extended.
</p>projecteuclid.org/euclid.afa/1538121758_20181102220101Fri, 02 Nov 2018 22:01 EDTOn summability of multilinear operators and applicationshttps://projecteuclid.org/euclid.afa/1540001195<strong>Nacib Albuquerque</strong>, <strong>Gustavo Araújo</strong>, <strong>Wasthenny Cavalcante</strong>, <strong>Tony Nogueira</strong>, <strong>Daniel Núñez</strong>, <strong>Daniel Pellegrino</strong>, <strong>Pilar Rueda</strong>. <p><strong>Source: </strong>Annals of Functional Analysis, Volume 9, Number 4, 574--590.</p><p><strong>Abstract:</strong><br/>
This article has two clear motivations, one technical and one practical. The technical motivation unifies in a single formulation a huge family of inequalities that have been produced separately over the last ninety years in different contexts. But we do not just join inequalities; our method also creates a family of inequalities that were invisible by previous approaches. The practical motivation is to show that our new approach has the strength to attack various problems. We provide new applications of our family of inequalities, continuing recent work by Maia, Nogueira, and Pellegrino.
</p>projecteuclid.org/euclid.afa/1540001195_20181102220101Fri, 02 Nov 2018 22:01 EDTCyclic weighted shift matrix with reversible weightshttps://projecteuclid.org/euclid.afa/1546506017<strong>Peng-Ruei Huang</strong>, <strong>Hiroshi Nakazato</strong>. <p><strong>Source: </strong>Annals of Functional Analysis, Advance publication, 9 pages.</p><p><strong>Abstract:</strong><br/>
We characterize a class of matrices that is unitarily similar to a complex symmetric matrix via the discrete Fourier transform.
</p>projecteuclid.org/euclid.afa/1546506017_20190103040038Thu, 03 Jan 2019 04:00 ESTOn extreme contractions and the norm attainment set of a bounded linear operatorhttps://projecteuclid.org/euclid.afa/1543309249<strong>Debmalya Sain</strong>. <p><strong>Source: </strong>Annals of Functional Analysis, Advance publication, 9 pages.</p><p><strong>Abstract:</strong><br/>
In this paper we completely characterize the norm attainment set of a bounded linear operator between Hilbert spaces. In fact, we obtain two different characterizations of the norm attainment set of a bounded linear operator between Hilbert spaces. We further study the extreme contractions on various types of finite-dimensional Banach spaces, namely Euclidean spaces, and strictly convex spaces. In particular, we give an elementary alternative proof of the well-known characterization of extreme contractions on a Euclidean space, which works equally well for both the real and the complex case. As an application of our exploration, we prove that it is possible to characterize real Hilbert spaces among real Banach spaces, in terms of extreme contractions on their $2$ -dimensional subspaces.
</p>projecteuclid.org/euclid.afa/1543309249_20190103040038Thu, 03 Jan 2019 04:00 ESTDoubly stochastic operators with zero entropyhttps://projecteuclid.org/euclid.afa/1542790825<strong>Bartosz Frej</strong>, <strong>Dawid Huczek</strong>. <p><strong>Source: </strong>Annals of Functional Analysis, Advance publication, 13 pages.</p><p><strong>Abstract:</strong><br/>
We study doubly stochastic operators with zero entropy. We generalize three famous theorems: Rokhlin’s theorem on genericity of zero entropy, Kushnirenko’s theorem on equivalence of discrete spectrum and nullity, and Halmos–von Neumann’s theorem on representation of maps with discrete spectrum as group rotations.
</p>projecteuclid.org/euclid.afa/1542790825_20190103040038Thu, 03 Jan 2019 04:00 ESTEmbedding theorems and integration operators on Bergman spaces with exponential weightshttps://projecteuclid.org/euclid.afa/1542790826<strong>Xiaofen Lv</strong>. <p><strong>Source: </strong>Annals of Functional Analysis, Advance publication, 13 pages.</p><p><strong>Abstract:</strong><br/>
In this article, given some positive Borel measure $\mu$ , we define two integration operators to be
\[I_{\mu}(f)(z)=\int_{\mathbf{D}}f(w)K(z,w)e^{-2\varphi(w)}\,d\mu(w)\] and
\[J_{\mu}(f)(z)=\int_{\mathbf{D}}\vert f(w)K(z,w)\vert e^{-2\varphi(w)}\,d\mu(w).\] We characterize the boundedness and compactness of these operators from the Bergman space $A^{p}_{\varphi}$ to $L^{q}_{\varphi}$ for $1\lt p,q\lt \infty$ , where $\varphi$ belongs to a large class ${\mathcal{W}}_{0}$ , which covers those defined by Borichev, Dhuez, and Kellay in 2007. We also completely describe those $\mu$ ’s such that the embedding operator is bounded or compact from $A^{p}_{\varphi}$ to $L^{q}_{\varphi}(d\mu)$ , $0\lt p,q\lt \infty$ .
</p>projecteuclid.org/euclid.afa/1542790826_20190103040038Thu, 03 Jan 2019 04:00 ESTUnitary representations of infinite wreath productshttps://projecteuclid.org/euclid.afa/1542423684<strong>Robert P. Boyer</strong>, <strong>Yun S. Yoo</strong>. <p><strong>Source: </strong>Annals of Functional Analysis, Advance publication, 9 pages.</p><p><strong>Abstract:</strong><br/>
Using $C^{*}$ -algebraic techniques and especially AF-algebras, we present a complete classification of the continuous unitary representations for a class of infinite wreath product groups. These nonlocally compact groups are realized by a topological completion of the semidirect product of the countably infinite symmetric group acting on the countable direct product of a finite Abelian group.
</p>projecteuclid.org/euclid.afa/1542423684_20190103040038Thu, 03 Jan 2019 04:00 ESTOn $J$ -frames related to maximal definite subspaceshttps://projecteuclid.org/euclid.afa/1542423685<strong>Alan Kamuda</strong>, <strong>Sergii Kuzhel</strong>. <p><strong>Source: </strong>Annals of Functional Analysis, Advance publication, 16 pages.</p><p><strong>Abstract:</strong><br/>
We propose a definition of frames in Krein spaces which generalizes the concept of $J$ -frames defined relatively recently by Giribet, Maestripieri, Martínez-Pería, and Massey. The difference consists in the fact that a $J$ -frame is related to maximal definite subspaces $\mathcal{M}_{\pm}$ which are not assumed to be uniformly definite. The latter allows us to extend the set of $J$ -frames. In particular, some $J$ -orthogonal Schauder bases can be interpreted as $J$ -frames.
</p>projecteuclid.org/euclid.afa/1542423685_20190103040038Thu, 03 Jan 2019 04:00 ESTUnique expectations for discrete crossed productshttps://projecteuclid.org/euclid.afa/1540454430<strong>Vrej Zarikian</strong>. <p><strong>Source: </strong>Annals of Functional Analysis, Advance publication, 12 pages.</p><p><strong>Abstract:</strong><br/>
Let $G$ be a discrete group acting on a unital $C^{*}$ -algebra $\mathcal{A}$ by $*$ -automorphisms. We characterize (in terms of the dynamics) when the inclusion $\mathcal{A}\subseteq\mathcal{A}\rtimes_{r}G$ has a unique conditional expectation, and when it has a unique pseudoexpectation in the sense of Pitts; we do likewise for the inclusion $\mathcal{A}\subseteq\mathcal{A}\rtimes G$ . As an application, we re-prove (and potentially extend) some known $C^{*}$ -simplicity results for $\mathcal{A}\rtimes_{r}G$ .
</p>projecteuclid.org/euclid.afa/1540454430_20190103040038Thu, 03 Jan 2019 04:00 ESTOn the structure of the dual unit ball of strict $u$ -idealshttps://projecteuclid.org/euclid.afa/1538121757<strong>Julia Martsinkevitš</strong>, <strong>Märt Põldvere</strong>. <p><strong>Source: </strong>Annals of Functional Analysis, Advance publication, 14 pages.</p><p><strong>Abstract:</strong><br/>
It is known that if a Banach space $Y$ is a $u$ -ideal in its bidual $Y^{\ast\ast}$ with respect to the canonical projection on the third dual $Y^{\ast\ast\ast}$ , then $Y^{\ast}$ contains “many” functionals admitting a unique norm-preserving extension to $Y^{\ast\ast}$ —the dual unit ball $B_{Y^{\ast}}$ is the norm-closed convex hull of its weak $^{\ast}$ strongly exposed points by a result of Å. Lima from 1995. We show that if $Y$ is a strict $u$ -ideal in a Banach space $X$ with respect to an ideal projection $P$ on $X^{\ast}$ , and $X/Y$ is separable, then $B_{Y^{\ast}}$ is the $\tau_{P}$ -closed convex hull of functionals admitting a unique norm-preserving extension to $X$ , where $\tau_{P}$ is a certain weak topology on $Y^{\ast}$ defined by the ideal projection $P$ .
</p>projecteuclid.org/euclid.afa/1538121757_20190103040038Thu, 03 Jan 2019 04:00 ESTThe rate of almost-everywhere convergence of Bochner–Riesz means on Sobolev spaceshttps://projecteuclid.org/euclid.afa/1531792882<strong>Junyan Zhao</strong>, <strong>Dashan Fan</strong>. <p><strong>Source: </strong>Annals of Functional Analysis, Advance publication, 17 pages.</p><p><strong>Abstract:</strong><br/>
We investigate the convergence rate of the generalized Bochner–Riesz means $S_{R}^{\delta,\gamma}$ on $L^{p}$ -Sobolev spaces in the sharp range of $\delta$ and $p$ ( $p\geq2$ ). We give the relation between the smoothness imposed on functions and the rate of almost-everywhere convergence of $S_{R}^{\delta,\gamma}$ . As an application, the corresponding results can be extended to the $n$ -torus $\mathbb{T}^{n}$ by using some transference theorems. Also, we consider the following two generalized Bochner–Riesz multipliers, $(1-\vert \xi \vert ^{\gamma_{1}})_{+}^{\delta}$ and $(1-\vert \xi \vert ^{\gamma_{2}})_{+}^{\delta}$ , where $\gamma_{1}$ , $\gamma_{2}$ , $\delta$ are positive real numbers. We prove that, as the maximal operators of the multiplier operators with respect to the two functions, their $L^{2}(|x|^{-\beta})$ -boundedness is equivalent for any $\gamma_{1}$ , $\gamma_{2}$ and fixed $\delta$ .
</p>projecteuclid.org/euclid.afa/1531792882_20190103040038Thu, 03 Jan 2019 04:00 ESTSurjectivity of coercive gradient operators in Hilbert space and nonlinear spectral theoryhttps://projecteuclid.org/euclid.afa/1531533617<strong>Raffaele Chiappinelli</strong>. <p><strong>Source: </strong>Annals of Functional Analysis, Advance publication, 10 pages.</p><p><strong>Abstract:</strong><br/>
We consider continuous gradient operators $F$ acting in a real Hilbert space $H$ , and we study their surjectivity under the basic assumption that the corresponding functional $\langle F(x),x\rangle $ —where $\langle \cdot \rangle $ is the scalar product in $H$ —is coercive. While this condition is sufficient in the case of a linear operator (where one in fact deals with a bounded self-adjoint operator), in the general case we supplement it with a compactness condition involving the number $\omega (F)$ introduced by Furi, Martelli, and Vignoli, whose positivity indeed guarantees that $F$ is proper on closed bounded sets of $H$ . We then use Ekeland’s variational principle to reach the desired conclusion. In the second part of this article, we apply the surjectivity result to give a perspective on the spectrum of these kinds of operators—ones not considered by Feng or the above authors—when they are further assumed to be sublinear and positively homogeneous.
</p>projecteuclid.org/euclid.afa/1531533617_20190103040038Thu, 03 Jan 2019 04:00 ESTDecompositions of completely bounded maps into completely positive maps involving trace class operatorshttps://projecteuclid.org/euclid.afa/1531533618<strong>Yuan Li</strong>, <strong>Mengqian Cui</strong>, <strong>Jiao Wu</strong>. <p><strong>Source: </strong>Annals of Functional Analysis, Advance publication, 13 pages.</p><p><strong>Abstract:</strong><br/>
Let $K\mathcal{(H)}$ and ${\mathcal{B(H)}}$ be the sets of all compact operators and all bounded linear operators, respectively, on the Hilbert space $\mathcal{H}$ . In this article, we mainly show that if $\Phi\in\operatorname{CB}(K{\mathcal{(H)}}^{*},\mathcal{B}{\mathcal{(K)}})$ , then there exist $\Phi_{i}\in\operatorname{CP}(K{\mathcal{(H)}}^{*},{\mathcal{B(K)}})$ , for $i=1,2,3,4$ , such that $\Phi=(\Phi_{1}-\Phi_{2})+\sqrt{-1}(\Phi_{3}-\Phi_{4})$ . However, $\operatorname{CP}(K{\mathcal{(H)}}^{*},{\mathcal{B(K)}})\nsubseteq\operatorname{CB}(K{\mathcal{(H)}}^{*},\mathcal{B}{\mathcal{(K)}})$ , where $\operatorname{CB}(V,W)$ and $\operatorname{CP}(V,W)$ are the sets of all completely bounded maps and all completely positive maps from $V$ into $W$ , respectively.
</p>projecteuclid.org/euclid.afa/1531533618_20190103040038Thu, 03 Jan 2019 04:00 ESTProduct of quasihomogeneous Toeplitz operators on the pluriharmonic Bergman space of the polydiskhttps://projecteuclid.org/euclid.afa/1531533621<strong>Cao Jiang</strong>, <strong>Xing-Tang Dong</strong>, <strong>Ze-Hua Zhou</strong>. <p><strong>Source: </strong>Annals of Functional Analysis, Advance publication, 15 pages.</p><p><strong>Abstract:</strong><br/>
In this article, we first give an essential characterization of Toeplitz operators with quasihomogeneous symbols on the weighted pluriharmonic Bergman space of the unit polydisk. Then we completely characterize when the product of two Toeplitz operators with monomial-type symbols is a Toeplitz operator. As a result, some interesting higher-dimensional phenomena appear on the unit polydisk.
</p>projecteuclid.org/euclid.afa/1531533621_20190103040038Thu, 03 Jan 2019 04:00 ESTI-convexity and Q-convexity in Orlicz–Bochner function spaces equipped with the Luxemburg normhttps://projecteuclid.org/euclid.afa/1546851657<strong>Wanzhong Gong</strong>, <strong>Xiaoli Dong</strong>, <strong>Kangji Wang</strong>. <p><strong>Source: </strong>Annals of Functional Analysis, Advance publication, 16 pages.</p><p><strong>Abstract:</strong><br/>
We study I-convexity and Q-convexity, two geometric properties introduced by Amir and Franchetti. We point out that a Banach space $X$ has the weak fixed-point property when $X$ is I-convex (or Q-convex) with a strongly bimonotone basis. By means of some characterizations of I-convexity and Q-convexity in Banach spaces, we obtain criteria for these two convexities in the Orlicz–Bochner function space $L_{(M)}(\mu,X)$ : that $L_{(M)}(\mu,X)$ is I-convex (or Q-convex) if and only if $L_{(M)}(\mu)$ is reflexive and $X$ is I-convex (or Q-convex).
</p>projecteuclid.org/euclid.afa/1546851657_20190107040117Mon, 07 Jan 2019 04:01 ESTFunction spaces of coercivity for the fractional Laplacian in spaces of homogeneous typehttps://projecteuclid.org/euclid.afa/1547542826<strong>Hugo Aimar</strong>, <strong>Ivana Gómez</strong>. <p><strong>Source: </strong>Annals of Functional Analysis, Advance publication, 13 pages.</p><p><strong>Abstract:</strong><br/>
We combine dyadic analysis through Haar-type wavelets (defined on Christ’s families of generalized cubes) and the Lax–Milgram theorem in order to prove the existence of Green’s functions for fractional Laplacians on some function spaces of vanishing small resolution in spaces of homogeneous type.
</p>projecteuclid.org/euclid.afa/1547542826_20190115040100Tue, 15 Jan 2019 04:01 ESTProduct of quasihomogeneous Toeplitz operators on the pluriharmonic Bergman space of the polydiskhttps://projecteuclid.org/euclid.afa/1547629219<strong>Cao Jiang</strong>, <strong>Xing-Tang Dong</strong>, <strong>Ze-Hua Zhou</strong>. <p><strong>Source: </strong>Annals of Functional Analysis, Volume 10, Number 1, 1--15.</p><p><strong>Abstract:</strong><br/>
In this article, we first give an essential characterization of Toeplitz operators with quasihomogeneous symbols on the weighted pluriharmonic Bergman space of the unit polydisk. Then we completely characterize when the product of two Toeplitz operators with monomial-type symbols is a Toeplitz operator. As a result, some interesting higher-dimensional phenomena appear on the unit polydisk.
</p>projecteuclid.org/euclid.afa/1547629219_20190116040031Wed, 16 Jan 2019 04:00 ESTDecompositions of completely bounded maps into completely positive maps involving trace class operatorshttps://projecteuclid.org/euclid.afa/1547629220<strong>Yuan Li</strong>, <strong>Mengqian Cui</strong>, <strong>Jiao Wu</strong>. <p><strong>Source: </strong>Annals of Functional Analysis, Volume 10, Number 1, 16--28.</p><p><strong>Abstract:</strong><br/>
Let $K\mathcal{(H)}$ and ${\mathcal{B(H)}}$ be the sets of all compact operators and all bounded linear operators, respectively, on the Hilbert space $\mathcal{H}$ . In this article, we mainly show that if $\Phi\in\operatorname{CB}(K{\mathcal{(H)}}^{*},\mathcal{B}{\mathcal{(K)}})$ , then there exist $\Phi_{i}\in\operatorname{CP}(K{\mathcal{(H)}}^{*},{\mathcal{B(K)}})$ , for $i=1,2,3,4$ , such that $\Phi=(\Phi_{1}-\Phi_{2})+\sqrt{-1}(\Phi_{3}-\Phi_{4})$ . However, $\operatorname{CP}(K{\mathcal{(H)}}^{*},{\mathcal{B(K)}})\nsubseteq\operatorname{CB}(K{\mathcal{(H)}}^{*},\mathcal{B}{\mathcal{(K)}})$ , where $\operatorname{CB}(V,W)$ and $\operatorname{CP}(V,W)$ are the sets of all completely bounded maps and all completely positive maps from $V$ into $W$ , respectively.
</p>projecteuclid.org/euclid.afa/1547629220_20190116040031Wed, 16 Jan 2019 04:00 ESTThe rate of almost-everywhere convergence of Bochner–Riesz means on Sobolev spaceshttps://projecteuclid.org/euclid.afa/1547629221<strong>Junyan Zhao</strong>, <strong>Dashan Fan</strong>. <p><strong>Source: </strong>Annals of Functional Analysis, Volume 10, Number 1, 29--45.</p><p><strong>Abstract:</strong><br/>
We investigate the convergence rate of the generalized Bochner–Riesz means $S_{R}^{\delta,\gamma}$ on $L^{p}$ -Sobolev spaces in the sharp range of $\delta$ and $p$ ( $p\geq2$ ). We give the relation between the smoothness imposed on functions and the rate of almost-everywhere convergence of $S_{R}^{\delta,\gamma}$ . As an application, the corresponding results can be extended to the $n$ -torus $\mathbb{T}^{n}$ by using some transference theorems. Also, we consider the following two generalized Bochner–Riesz multipliers, $(1-\vert \xi \vert ^{\gamma_{1}})_{+}^{\delta}$ and $(1-\vert \xi \vert ^{\gamma_{2}})_{+}^{\delta}$ , where $\gamma_{1}$ , $\gamma_{2}$ , $\delta$ are positive real numbers. We prove that, as the maximal operators of the multiplier operators with respect to the two functions, their $L^{2}(|x|^{-\beta})$ -boundedness is equivalent for any $\gamma_{1}$ , $\gamma_{2}$ and fixed $\delta$ .
</p>projecteuclid.org/euclid.afa/1547629221_20190116040031Wed, 16 Jan 2019 04:00 ESTOn the structure of the dual unit ball of strict $u$ -idealshttps://projecteuclid.org/euclid.afa/1547629222<strong>Julia Martsinkevitš</strong>, <strong>Märt Põldvere</strong>. <p><strong>Source: </strong>Annals of Functional Analysis, Volume 10, Number 1, 46--59.</p><p><strong>Abstract:</strong><br/>
It is known that if a Banach space $Y$ is a $u$ -ideal in its bidual $Y^{\ast\ast}$ with respect to the canonical projection on the third dual $Y^{\ast\ast\ast}$ , then $Y^{\ast}$ contains “many” functionals admitting a unique norm-preserving extension to $Y^{\ast\ast}$ —the dual unit ball $B_{Y^{\ast}}$ is the norm-closed convex hull of its weak $^{\ast}$ strongly exposed points by a result of Å. Lima from 1995. We show that if $Y$ is a strict $u$ -ideal in a Banach space $X$ with respect to an ideal projection $P$ on $X^{\ast}$ , and $X/Y$ is separable, then $B_{Y^{\ast}}$ is the $\tau_{P}$ -closed convex hull of functionals admitting a unique norm-preserving extension to $X$ , where $\tau_{P}$ is a certain weak topology on $Y^{\ast}$ defined by the ideal projection $P$ .
</p>projecteuclid.org/euclid.afa/1547629222_20190116040031Wed, 16 Jan 2019 04:00 ESTUnique expectations for discrete crossed productshttps://projecteuclid.org/euclid.afa/1547629223<strong>Vrej Zarikian</strong>. <p><strong>Source: </strong>Annals of Functional Analysis, Volume 10, Number 1, 60--71.</p><p><strong>Abstract:</strong><br/>
Let $G$ be a discrete group acting on a unital $C^{*}$ -algebra $\mathcal{A}$ by $*$ -automorphisms. We characterize (in terms of the dynamics) when the inclusion $\mathcal{A}\subseteq\mathcal{A}\rtimes_{r}G$ has a unique conditional expectation, and when it has a unique pseudoexpectation in the sense of Pitts; we do likewise for the inclusion $\mathcal{A}\subseteq\mathcal{A}\rtimes G$ . As an application, we re-prove (and potentially extend) some known $C^{*}$ -simplicity results for $\mathcal{A}\rtimes_{r}G$ .
</p>projecteuclid.org/euclid.afa/1547629223_20190116040031Wed, 16 Jan 2019 04:00 ESTCyclic weighted shift matrix with reversible weightshttps://projecteuclid.org/euclid.afa/1547629224<strong>Peng-Ruei Huang</strong>, <strong>Hiroshi Nakazato</strong>. <p><strong>Source: </strong>Annals of Functional Analysis, Volume 10, Number 1, 72--80.</p><p><strong>Abstract:</strong><br/>
We characterize a class of matrices that is unitarily similar to a complex symmetric matrix via the discrete Fourier transform.
</p>projecteuclid.org/euclid.afa/1547629224_20190116040031Wed, 16 Jan 2019 04:00 ESTI-convexity and Q-convexity in Orlicz–Bochner function spaces equipped with the Luxemburg normhttps://projecteuclid.org/euclid.afa/1547629225<strong>Wanzhong Gong</strong>, <strong>Xiaoli Dong</strong>, <strong>Kangji Wang</strong>. <p><strong>Source: </strong>Annals of Functional Analysis, Volume 10, Number 1, 81--96.</p><p><strong>Abstract:</strong><br/>
We study I-convexity and Q-convexity, two geometric properties introduced by Amir and Franchetti. We point out that a Banach space $X$ has the weak fixed-point property when $X$ is I-convex (or Q-convex) with a strongly bimonotone basis. By means of some characterizations of I-convexity and Q-convexity in Banach spaces, we obtain criteria for these two convexities in the Orlicz–Bochner function space $L_{(M)}(\mu,X)$ : that $L_{(M)}(\mu,X)$ is I-convex (or Q-convex) if and only if $L_{(M)}(\mu)$ is reflexive and $X$ is I-convex (or Q-convex).
</p>projecteuclid.org/euclid.afa/1547629225_20190116040031Wed, 16 Jan 2019 04:00 ESTUnitary representations of infinite wreath productshttps://projecteuclid.org/euclid.afa/1547629226<strong>Robert P. Boyer</strong>, <strong>Yun S. Yoo</strong>. <p><strong>Source: </strong>Annals of Functional Analysis, Volume 10, Number 1, 97--105.</p><p><strong>Abstract:</strong><br/>
Using $C^{*}$ -algebraic techniques and especially AF-algebras, we present a complete classification of the continuous unitary representations for a class of infinite wreath product groups. These nonlocally compact groups are realized by a topological completion of the semidirect product of the countably infinite symmetric group acting on the countable direct product of a finite Abelian group.
</p>projecteuclid.org/euclid.afa/1547629226_20190116040031Wed, 16 Jan 2019 04:00 ESTOn $J$ -frames related to maximal definite subspaceshttps://projecteuclid.org/euclid.afa/1547629227<strong>Alan Kamuda</strong>, <strong>Sergii Kuzhel</strong>. <p><strong>Source: </strong>Annals of Functional Analysis, Volume 10, Number 1, 106--121.</p><p><strong>Abstract:</strong><br/>
We propose a definition of frames in Krein spaces which generalizes the concept of $J$ -frames defined relatively recently by Giribet, Maestripieri, Martínez-Pería, and Massey. The difference consists in the fact that a $J$ -frame is related to maximal definite subspaces $\mathcal{M}_{\pm}$ which are not assumed to be uniformly definite. The latter allows us to extend the set of $J$ -frames. In particular, some $J$ -orthogonal Schauder bases can be interpreted as $J$ -frames.
</p>projecteuclid.org/euclid.afa/1547629227_20190116040031Wed, 16 Jan 2019 04:00 ESTEmbedding theorems and integration operators on Bergman spaces with exponential weightshttps://projecteuclid.org/euclid.afa/1547629228<strong>Xiaofen Lv</strong>. <p><strong>Source: </strong>Annals of Functional Analysis, Volume 10, Number 1, 122--134.</p><p><strong>Abstract:</strong><br/>
In this article, given some positive Borel measure $\mu$ , we define two integration operators to be
\[I_{\mu}(f)(z)=\int_{\mathbf{D}}f(w)K(z,w)e^{-2\varphi(w)}\,d\mu(w)\] and
\[J_{\mu}(f)(z)=\int_{\mathbf{D}}\vert f(w)K(z,w)\vert e^{-2\varphi(w)}\,d\mu(w).\] We characterize the boundedness and compactness of these operators from the Bergman space $A^{p}_{\varphi}$ to $L^{q}_{\varphi}$ for $1\lt p,q\lt \infty$ , where $\varphi$ belongs to a large class ${\mathcal{W}}_{0}$ , which covers those defined by Borichev, Dhuez, and Kellay in 2007. We also completely describe those $\mu$ ’s such that the embedding operator is bounded or compact from $A^{p}_{\varphi}$ to $L^{q}_{\varphi}(d\mu)$ , $0\lt p,q\lt \infty$ .
</p>projecteuclid.org/euclid.afa/1547629228_20190116040031Wed, 16 Jan 2019 04:00 ESTOn extreme contractions and the norm attainment set of a bounded linear operatorhttps://projecteuclid.org/euclid.afa/1547629229<strong>Debmalya Sain</strong>. <p><strong>Source: </strong>Annals of Functional Analysis, Volume 10, Number 1, 135--143.</p><p><strong>Abstract:</strong><br/>
In this paper we completely characterize the norm attainment set of a bounded linear operator between Hilbert spaces. In fact, we obtain two different characterizations of the norm attainment set of a bounded linear operator between Hilbert spaces. We further study the extreme contractions on various types of finite-dimensional Banach spaces, namely Euclidean spaces, and strictly convex spaces. In particular, we give an elementary alternative proof of the well-known characterization of extreme contractions on a Euclidean space, which works equally well for both the real and the complex case. As an application of our exploration, we prove that it is possible to characterize real Hilbert spaces among real Banach spaces, in terms of extreme contractions on their $2$ -dimensional subspaces.
</p>projecteuclid.org/euclid.afa/1547629229_20190116040031Wed, 16 Jan 2019 04:00 ESTDoubly stochastic operators with zero entropyhttps://projecteuclid.org/euclid.afa/1547629230<strong>Bartosz Frej</strong>, <strong>Dawid Huczek</strong>. <p><strong>Source: </strong>Annals of Functional Analysis, Volume 10, Number 1, 144--156.</p><p><strong>Abstract:</strong><br/>
We study doubly stochastic operators with zero entropy. We generalize three famous theorems: Rokhlin’s theorem on genericity of zero entropy, Kushnirenko’s theorem on equivalence of discrete spectrum and nullity, and Halmos–von Neumann’s theorem on representation of maps with discrete spectrum as group rotations.
</p>projecteuclid.org/euclid.afa/1547629230_20190116040031Wed, 16 Jan 2019 04:00 ESTG-frames and their generalized multipliers in Hilbert spaceshttps://projecteuclid.org/euclid.afa/1548126085<strong>Hessam Hosseinnezhad</strong>, <strong>Gholamreza Abbaspour Tabadkan</strong>, <strong>Asghar Rahimi</strong>. <p><strong>Source: </strong>Annals of Functional Analysis, Volume 10, Number 2, 180--195.</p><p><strong>Abstract:</strong><br/>
In this article, we introduce the concept of generalized multipliers for g-frames. In fact, we show that every generalized multiplier for g-Bessel sequences is a generalized multiplier for the induced sequences, in a special sense. We provide some sufficient and/or necessary conditions for the invertibility of generalized multipliers. In particular, we characterize g-Riesz bases by invertible multipliers. We look at which perturbations of g-Bessel sequences preserve the invertibility of generalized multipliers. Finally, we investigate how to find a matrix representation of operators on a Hilbert space using g-frames, and then we characterize g-Riesz bases and g-orthonormal bases by applying such matrices.
</p>projecteuclid.org/euclid.afa/1548126085_20190419040218Fri, 19 Apr 2019 04:02 EDTOrthogonal complementing in Hilbert $C^{*}$ -moduleshttps://projecteuclid.org/euclid.afa/1552960868<strong>Boris Guljaš</strong>. <p><strong>Source: </strong>Annals of Functional Analysis, Volume 10, Number 2, 196--202.</p><p><strong>Abstract:</strong><br/>
We characterize orthogonally complemented submodules in Hilbert $C^{*}$ -modules by their orthogonal closures. Applying Magajna’s characterization of Hilbert $C^{*}$ -modules over $C^{*}$ -algebras of compact operators by the complementing property of submodules, we give an elementary proof of Schweizer’s characterization of Hilbert $C^{*}$ -modules over $C^{*}$ -algebras of compact operators. Also, we prove analogous characterization theorems for $C^{*}$ -algebras of compact operators related to topological properties of submodules of strict completions of Hilbert modules over a nonunital $C^{*}$ -algebra.
</p>projecteuclid.org/euclid.afa/1552960868_20190419040218Fri, 19 Apr 2019 04:02 EDTOn graph algebras from interval mapshttps://projecteuclid.org/euclid.afa/1552960867<strong>C. Correia Ramos</strong>, <strong>Nuno Martins</strong>, <strong>Paulo R. Pinto</strong>. <p><strong>Source: </strong>Annals of Functional Analysis, Volume 10, Number 2, 203--217.</p><p><strong>Abstract:</strong><br/>
We produce and study a family of representations of relative graph algebras on Hilbert spaces that arise from the orbits of points of $1$ -dimensional dynamical systems, where the underlying Markov interval maps $f$ have escape sets. We identify when such representations are faithful in terms of the transitions to the escape subintervals.
</p>projecteuclid.org/euclid.afa/1552960867_20190419040218Fri, 19 Apr 2019 04:02 EDTA note on peripherally multiplicative maps on Banach algebrashttps://projecteuclid.org/euclid.afa/1552960866<strong>Francois Schulz</strong>. <p><strong>Source: </strong>Annals of Functional Analysis, Volume 10, Number 2, 218--228.</p><p><strong>Abstract:</strong><br/>
Let $A$ and $B$ be complex Banach algebras, and let $\phi,\phi_{1}$ , and $\phi_{2}$ be surjective maps from $A$ onto $B$ . Denote by $\partial\sigma(x)$ the boundary of the spectrum of $x$ . If $A$ is semisimple, $B$ has an essential socle, and $\partial\sigma(xy)=\partial\sigma(\phi_{1}(x)\phi_{2}(y))$ for each $x,y\in A$ , then we prove that the maps $x\mapsto\phi_{1}(\mathbf{1})\phi_{2}(x)$ and $x\mapsto\phi_{1}(x)\phi_{2}(\mathbf{1})$ coincide and are continuous Jordan isomorphisms. Moreover, if $A$ is prime with nonzero socle and $\phi_{1}$ and $\phi_{2}$ satisfy the aforementioned condition, then we show once again that the maps $x\mapsto\phi_{1}(\mathbf{1})\phi_{2}(x)$ and $x\mapsto\phi_{1}(x)\phi_{2}(\mathbf{1})$ coincide and are continuous. However, in this case we conclude that the maps are either isomorphisms or anti-isomorphisms. Finally, if $A$ is prime with nonzero socle and $\phi$ is a peripherally multiplicative map, then we prove that $\phi$ is continuous and either $\phi$ or $-\phi$ is an isomorphism or an anti-isomorphism.
</p>projecteuclid.org/euclid.afa/1552960866_20190419040218Fri, 19 Apr 2019 04:02 EDTOn Weyl completions of partial operator matriceshttps://projecteuclid.org/euclid.afa/1552960865<strong>Xiufeng Wu</strong>, <strong>Junjie Huang</strong>, <strong>Alatancang Chen</strong>. <p><strong>Source: </strong>Annals of Functional Analysis, Volume 10, Number 2, 229--241.</p><p><strong>Abstract:</strong><br/>
Let $\mathcal{H}$ and $\mathcal{K}$ be complex separable Hilbert spaces. Given the operators $A\in \mathcal{B}(\mathcal{H})$ and $B\in\mathcal{B}(\mathcal{K},\mathcal{H})$ , we define $M_{X,Y}:=[\begin{smallmatrix}A&B\\X&Y\end{smallmatrix}]$ , where $X\in \mathcal{B}(\mathcal{H},\mathcal{K})$ and $Y\in\mathcal{B}(\mathcal{K})$ are unknown elements. In this article, we give a necessary and sufficient condition for $M_{X,Y}$ to be a (right) Weyl operator for some $X\in \mathcal{B}(\mathcal{H},\mathcal{K})$ and $Y\in \mathcal{B}(\mathcal{K})$ . Moreover, we show that if $\dim \mathcal{K}\lt \infty $ , then $M_{X,Y}$ is a left Weyl operator for some $X\in \mathcal{B}(\mathcal{H},\mathcal{K})$ and $Y\in\mathcal{B}(\mathcal{K})$ if and only if $[A\ B]$ is a left Fredholm operator and $\operatorname{ind}([A\ B])\leq \dim \mathcal{K}$ ; if $\dim \mathcal{K}=\infty $ , then $M_{X,Y}$ is a left Weyl operator for some $X\in \mathcal{B}(\mathcal{H},\mathcal{K})$ and $Y\in \mathcal{B}(\mathcal{K})$ .
</p>projecteuclid.org/euclid.afa/1552960865_20190419040218Fri, 19 Apr 2019 04:02 EDTThe structure of 2-local Lie derivations on von Neumann algebrashttps://projecteuclid.org/euclid.afa/1552960864<strong>Bing Yang</strong>, <strong>Xiaochun Fang</strong>. <p><strong>Source: </strong>Annals of Functional Analysis, Volume 10, Number 2, 242--251.</p><p><strong>Abstract:</strong><br/>
In this article we characterize the form of each 2-local Lie derivation on a von Neumann algebra without central summands of type ${I_{1}}$ . We deduce that every 2-local Lie derivation $\delta$ on a finite von Neumann algebra $\mathcal{M}$ without central summands of type ${I_{1}}$ can be written in the form $\delta(A)=AE-EA+h(A)$ for all $A$ in $\mathcal{M}$ , where $E$ is an element in $\mathcal{M}$ and $h$ is a center-valued homogenous mapping which annihilates each commutator of $\mathcal{M}$ . In particular, every linear 2-local Lie derivation is a Lie derivation on a finite von Neumann algebra without central summands of type ${I_{1}}$ . We also show that every 2-local Lie derivation on a properly infinite von Neumann algebra is a Lie derivation.
</p>projecteuclid.org/euclid.afa/1552960864_20190419040218Fri, 19 Apr 2019 04:02 EDTRefining and reversing the Fenchel inequality in convex analysishttps://projecteuclid.org/euclid.afa/1552960863<strong>Mustapha Raïssouli</strong>. <p><strong>Source: </strong>Annals of Functional Analysis, Volume 10, Number 2, 252--261.</p><p><strong>Abstract:</strong><br/>
Our main goal in this article is to give some functional inequalities involving a (convex) functional and its Fenchel conjugate. As a consequence, we obtain some refinements of the so-called Fenchel inequality as well as its reverse. Inequalities of interest illustrating the previous theoretical results are provided as well.
</p>projecteuclid.org/euclid.afa/1552960863_20190419040218Fri, 19 Apr 2019 04:02 EDTPartial hypoellipticity for a class of abstract differential complexes on Banach space scaleshttps://projecteuclid.org/euclid.afa/1553241620<strong>E. R. Aragão-Costa</strong>. <p><strong>Source: </strong>Annals of Functional Analysis, Volume 10, Number 2, 262--276.</p><p><strong>Abstract:</strong><br/>
In this article we give sufficient conditions for the hypoellipticity in the first level of the abstract complex generated by the differential operators $L_{j}=\frac{\partial}{\partial t_{j}}+\frac{\partial\phi}{\partialt_{j}}(t,A)A$ , $j=1,2,\ldots,n$ , where $A:D(A)\subset X\longrightarrow X$ is a sectorial operator in a Banach space $X$ , with $\Re\sigma(A)\gt 0$ , and $\phi=\phi(t,A)$ is a series of nonnegative powers of $A^{-1}$ with coefficients in $C^{\infty}(\Omega)$ , $\Omega$ being an open set of ${\mathbb{R}}^{n}$ with $n\in{\mathbb{N}}$ arbitrary. Analogous complexes have been studied by several authors in this field, but only in the case $n=1$ and with $X$ a Hilbert space. Therefore, in this article, we provide an improvement of these results by treating the question in a more general setup. First, we provide sufficient conditions to get the partial hypoellipticity for that complex in the elliptic region. Second, we study the particular operator $A=1-\Delta:W^{2,p}({\mathbb{R}}^{N})\subset L^{p}({\mathbb{R}}^{N})\longrightarrow L^{p}({\mathbb{R}}^{N})$ , for $1\leq p\leq2$ , which will allow us to solve the problem of points which do not belong to the elliptic region.
</p>projecteuclid.org/euclid.afa/1553241620_20190419040218Fri, 19 Apr 2019 04:02 EDTOn the equivalence of some concepts in the theory of Banach algebrashttps://projecteuclid.org/euclid.afa/1553241619<strong>Józef Banaś</strong>, <strong>Leszek Olszowy</strong>. <p><strong>Source: </strong>Annals of Functional Analysis, Volume 10, Number 2, 277--283.</p><p><strong>Abstract:</strong><br/>
Our principal aim in this article is to show the equivalence of two concepts used recently in the theory of Banach algebras. The result we present here solves an open problem raised by Jeribi and Krichen in their 2015 book.
</p>projecteuclid.org/euclid.afa/1553241619_20190419040218Fri, 19 Apr 2019 04:02 EDTThe Tychonoff theorem and invariant pseudodistanceshttps://projecteuclid.org/euclid.afa/1553241618<strong>Tadeusz Kuczumow</strong>, <strong>Stanisław Prus</strong>. <p><strong>Source: </strong>Annals of Functional Analysis, Volume 10, Number 2, 284--290.</p><p><strong>Abstract:</strong><br/>
In this article we introduce a method of constructing functions with claimed properties by using the Tychonoff theorem. As an application of this method we show that the Carathéodory distance $c_{D}$ of convex domains $D$ in a complex, locally convex, Hausdorff, and infinite-dimensional topological vector space is approximated by the Carathéodory distances $c_{D\cap Y}$ in finite-dimensional linear subspaces $Y$ . Originally this result is due to Dineen, Timoney, and Vigué who apply ultrafilters in their proof.
</p>projecteuclid.org/euclid.afa/1553241618_20190419040218Fri, 19 Apr 2019 04:02 EDT