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 ESTLim’s center and fixed-point theorems for isometry mappingshttps://projecteuclid.org/euclid.afa/1507881623<strong>S. Rajesh</strong>, <strong>P. Veeramani</strong>. <p><strong>Source: </strong>Annals of Functional Analysis, Advance publication, 12 pages.</p><p><strong>Abstract:</strong><br/>
In this article, we prove that if $K$ is a nonempty weakly compact convex set in a Banach space such that $K$ has the hereditary fixed-point property (FPP) and $\mathfrak{F}$ is a commuting family of isometry mappings on $K$ , then there exists a point in $C(K)$ which is fixed by every member in $\mathfrak{F}$ whenever $C(K)$ is a compact set. Also, we give an example to show that $C(K)$ , the Chebyshev center of $K$ , need not be invariant under isometry maps. This example answers the question as to whether the Chebyshev center is invariant under isometry maps. Furthermore, we give a simple example to illustrate that Lim’s center, as introduced by Lim, is different from the Chebyshev center.
</p>projecteuclid.org/euclid.afa/1507881623_20180104220516Thu, 04 Jan 2018 22:05 ESTCentral Calderón–Zygmund operators on Herz-type Hardy spaces of variable smoothness and integrabilityhttps://projecteuclid.org/euclid.afa/1507860330<strong>Alexander Meskhi</strong>, <strong>Humberto Rafeiro</strong>, <strong>Muhammad Asad Zaighum</strong>. <p><strong>Source: </strong>Annals of Functional Analysis, Advance publication, 12 pages.</p><p><strong>Abstract:</strong><br/>
In this article we use the atomic decomposition of a Herz-type Hardy space of variable smoothness and integrability to obtain the boundedness of the central Calderón–Zygmund operators on Herz-type Hardy spaces with variable smoothness and integrability.
</p>projecteuclid.org/euclid.afa/1507860330_20180104220516Thu, 04 Jan 2018 22:05 ESTEssential norm of the composition operators on the general spaces $H_{\omega,p}$ of Hardy spaceshttps://projecteuclid.org/euclid.afa/1507708815<strong>S. Rezaei</strong>. <p><strong>Source: </strong>Annals of Functional Analysis, Advance publication, 10 pages.</p><p><strong>Abstract:</strong><br/>
We obtain estimates for the essential norm of the composition operators acting on the general spaces $H_{\omega,p}$ of Hardy spaces. Our characterization is given in terms of generalized Nevanlinna counting functions.
</p>projecteuclid.org/euclid.afa/1507708815_20180104220516Thu, 04 Jan 2018 22:05 ESTOn an approximation of $2$ -dimensional Walsh–Fourier series in martingale Hardy spaceshttps://projecteuclid.org/euclid.afa/1507169076<strong>L. E. Persson</strong>, <strong>G. Tephnadze</strong>, <strong>P. Wall</strong>. <p><strong>Source: </strong>Annals of Functional Analysis, Advance publication, 14 pages.</p><p><strong>Abstract:</strong><br/>
In this paper, we investigate convergence and divergence of partial sums with respect to the $2$ -dimensional Walsh system on the martingale Hardy spaces. In particular, we find some conditions for the modulus of continuity which provide convergence of partial sums of Walsh–Fourier series. We also show that these conditions are in a sense necessary and sufficient.
</p>projecteuclid.org/euclid.afa/1507169076_20180104220516Thu, 04 Jan 2018 22:05 ESTOn the $p$ -Schur property of Banach spaceshttps://projecteuclid.org/euclid.afa/1507169077<strong>Mohammad B. Dehghani</strong>, <strong>S. Mohammad Moshtaghioun</strong>. <p><strong>Source: </strong>Annals of Functional Analysis, Advance publication, 14 pages.</p><p><strong>Abstract:</strong><br/>
We introduce the notion of the $p$ -Schur property ( $1\leq p\leq\infty$ ) as a generalization of the Schur property of Banach spaces, and then we present a number of basic properties and some examples. We also study its relation with some geometric properties of Banach spaces, such as the Gelfand–Phillips property. Moreover, we verify some necessary and sufficient conditions for the $p$ -Schur property of some closed subspaces of operator spaces.
</p>projecteuclid.org/euclid.afa/1507169077_20180104220516Thu, 04 Jan 2018 22:05 ESTOn the modulus of disjointness-preserving operators and $b$ - $AM$ -compact operators on Banach latticeshttps://projecteuclid.org/euclid.afa/1502697620<strong>Kazem Haghnezhad Azar</strong>, <strong>Razi Alavizadeh</strong>. <p><strong>Source: </strong>Annals of Functional Analysis, Advance publication, 10 pages.</p><p><strong>Abstract:</strong><br/>
We study several properties of the modulus of order bounded disjointness-preserving operators. We show that, if $T$ is an order bounded disjointness-preserving operator, then $T$ and $\vert T\vert $ have the same compactness property for several types of compactness. Finally, we characterize Banach lattices having $b$ - $\mathit{AM}$ -compact (resp., $\mathit{AM}$ -compact) operators defined between them as having a modulus that is $b$ - $\mathit{AM}$ -compact (resp., $\mathit{AM}$ -compact).
</p>projecteuclid.org/euclid.afa/1502697620_20180104220516Thu, 04 Jan 2018 22:05 ESTOn solving proximal split feasibility problems and applicationshttps://projecteuclid.org/euclid.afa/1502697621<strong>Uamporn Witthayarat</strong>, <strong>Yeol Je Cho</strong>, <strong>Prasit Cholamjiak</strong>. <p><strong>Source: </strong>Annals of Functional Analysis, Advance publication, 12 pages.</p><p><strong>Abstract:</strong><br/>
We study the problem of proximal split feasibility of two objective convex functions in Hilbert spaces. We prove that, under suitable conditions, certain strong convergence theorems of the Halpern-type algorithm present solutions to the proximal split feasibility problem. Finally, we provide some related applications as well as numerical experiments.
</p>projecteuclid.org/euclid.afa/1502697621_20180104220516Thu, 04 Jan 2018 22:05 ESTAtomic decomposition of variable Hardy spaces via Littlewood–Paley–Stein theoryhttps://projecteuclid.org/euclid.afa/1502697622<strong>Jian Tan</strong>. <p><strong>Source: </strong>Annals of Functional Analysis, Advance publication, 14 pages.</p><p><strong>Abstract:</strong><br/>
The purpose of this paper is to give a new atomic decomposition for variable Hardy spaces via the discrete Littlewood–Paley–Stein theory. As an application of this decomposition, we assume that $T$ is a linear operator bounded on $L^{q}$ and $H^{p(\cdot)}$ , and we thus obtain that $T$ can be extended to a bounded operator from $H^{p(\cdot)}$ to $L^{p(\cdot)}$ .
</p>projecteuclid.org/euclid.afa/1502697622_20180104220516Thu, 04 Jan 2018 22:05 ESTScattered locally $C^{\ast}$ -algebrashttps://projecteuclid.org/euclid.afa/1499824814<strong>Maria Joiţa</strong>. <p><strong>Source: </strong>Annals of Functional Analysis, Advance publication, 11 pages.</p><p><strong>Abstract:</strong><br/>
In this article, we introduce the notion of a scattered locally $C^{\ast}$ -algebra and we give the conditions for a locally $C^{\ast}$ -algebra to be scattered. Given an action $\alpha$ of a locally compact group $G$ on a scattered locally $C^{\ast}$ -algebra $A[\tau_{\Gamma}]$ , it is natural to ask under what conditions the crossed product $A[\tau_{\Gamma}]\times_{\alpha}G$ is also scattered. We obtain some results concerning this question.
</p>projecteuclid.org/euclid.afa/1499824814_20180104220516Thu, 04 Jan 2018 22:05 ESTA new algorithm for the symmetric solution of the matrix equations $AXB=E$ and $CXD=F$https://projecteuclid.org/euclid.afa/1499824815<strong>Chunmei Li</strong>, <strong>Xuefeng Duan</strong>, <strong>Juan Li</strong>, <strong>Sitting Yu</strong>. <p><strong>Source: </strong>Annals of Functional Analysis, Advance publication, 9 pages.</p><p><strong>Abstract:</strong><br/>
We propose a new iterative algorithm to compute the symmetric solution of the matrix equations $AXB=E$ and $CXD=F$ . The greatest advantage of this new algorithm is higher speed and lower computational cost at each step compared with existing numerical algorithms. We state the solutions of these matrix equations as the intersection point of some closed convex sets, and then we use the alternating projection method to solve them. Finally, we use some numerical examples to show that the new algorithm is feasible and effective.
</p>projecteuclid.org/euclid.afa/1499824815_20180104220516Thu, 04 Jan 2018 22:05 ESTPerturbation bounds for the Moore–Penrose metric generalized inverse in some Banach spaceshttps://projecteuclid.org/euclid.afa/1499824816<strong>Jianbing Cao</strong>, <strong>Wanqin Zhang</strong>. <p><strong>Source: </strong>Annals of Functional Analysis, Advance publication, 13 pages.</p><p><strong>Abstract:</strong><br/>
Let $X,Y$ be Banach spaces, and let $T$ , $\delta T:X\to Y$ be bounded linear operators. Put $\bar{T}=T+\delta T$ . In this article, utilizing the gap between closed subspaces and the perturbation bounds of metric projections, we first present some error estimates of the upper bound of $\Vert \bar{T}^{M}-T^{M}\Vert $ in $L^{p}$ ( $1\lt p\lt +\infty$ ) spaces. Then, by using the concept of strong uniqueness and modulus of convexity, we further investigate the corresponding perturbation bound $\Vert \bar{T}^{M}-T^{M}\Vert $ in uniformly convex Banach spaces.
</p>projecteuclid.org/euclid.afa/1499824816_20180104220516Thu, 04 Jan 2018 22:05 ESTInhomogeneous Lipschitz spaces of variable order and their applicationshttps://projecteuclid.org/euclid.afa/1498723215<strong>Jian Tan</strong>, <strong>Jiman Zhao</strong>. <p><strong>Source: </strong>Annals of Functional Analysis, Advance publication, 15 pages.</p><p><strong>Abstract:</strong><br/>
In this article, the authors first give a Littlewood–Paley characterization for inhomogeneous Lipschitz spaces of variable order with the help of inhomogeneous Calderón identity and almost-orthogonality estimates. As applications, the boundedness of inhomogeneous Calderón–Zygmund singular integral operators of order $(\epsilon,\sigma)$ on these spaces has been presented. Finally, we note that a class of pseudodifferential operators $T_{a}\in\mathcal{O}pS_{1,1}^{0}$ are continuous on the inhomogeneous Lipschitz spaces of variable order as a corollary. We may observe that those operators are not, in general, continuous in $L^{2}$ .
</p>projecteuclid.org/euclid.afa/1498723215_20180104220516Thu, 04 Jan 2018 22:05 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 EST