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 ESTCharacter amenability and contractibility of some Banach algebras on left coset spaceshttp://projecteuclid.org/euclid.afa/1472659942<strong>M. Ramezanpour</strong>, <strong>N. Tavallaei</strong>, <strong>B. Olfatian Gillan</strong>. <p><strong>Source: </strong>Annals of Functional Analysis, Volume 7, Number 4, 564--572.</p><p><strong>Abstract:</strong><br/>
Let $H$ be a compact subgroup of a locally compact group $G$ , and let $\mu$ be a strongly quasi-invariant Radon measure on the homogeneous space $G/H$ . In this article, we show that every element of $\widehat{G/H}$ , the character space of $G/H$ , determines a nonzero multiplicative linear functional on $L^{1}(G/H,\mu)$ . Using this, we prove that for all $\phi\in\widehat{G/H}$ , the right $\phi$ -amenability of $L^{1}(G/H,\mu)$ and the right $\phi$ -amenability of $M(G/H)$ are both equivalent to the amenability of $G$ . Also, we show that $L^{1}(G/H,\mu)$ , as well as $M(G/H)$ , is right $\phi$ -contractible if and only if $G$ is compact. In particular, when $H$ is the trivial subgroup, we obtain the known results on group algebras and measure algebras.
</p>projecteuclid.org/euclid.afa/1472659942_20160831121224Wed, 31 Aug 2016 12:12 EDTA note on weak $^{*}$ -convergence in $h^{1}(\mathbb{R}^{d})$http://projecteuclid.org/euclid.afa/1472659943<strong>Ha Duy Hung</strong>, <strong>Duong Quoc Huy</strong>, <strong>Luong Dang Ky</strong>. <p><strong>Source: </strong>Annals of Functional Analysis, Volume 7, Number 4, 573--577.</p><p><strong>Abstract:</strong><br/>
We give a very simple proof of a result by Dafni
that states that the weak $^{*}$ -convergence is true in the local Hardy space $h^{1}(\mathbb{R}^{d})$ .
</p>projecteuclid.org/euclid.afa/1472659943_20160831121224Wed, 31 Aug 2016 12:12 EDTExtremally rich JB $^{*}$ -tripleshttp://projecteuclid.org/euclid.afa/1474652183<strong>Fatmah B. Jamjoom</strong>, <strong>Antonio M. Peralta</strong>, <strong>Akhlaq A. Siddiqui</strong>, <strong>Haifa M. Tahlawi</strong>. <p><strong>Source: </strong>Annals of Functional Analysis, Volume 7, Number 4, 578--592.</p><p><strong>Abstract:</strong><br/>
We introduce and study the class of extremally rich JB $^{*}$ -triples. We establish new results to determine the distance from an element $a$ in an extremally rich JB $^{*}$ -triple $E$ to the set $\partial_{e}(E_{1})$ of all extreme points of the closed unit ball of $E$ . More concretely, we prove that
\[\operatorname{dist}(a,\partial_{e}(E_{1}))=\max \{1,\|a\|-1\},\] for every $a\in E$ which is not Brown–Pedersen quasi-invertible. As a consequence, we determine the form of the $\lambda$ -function of Aron and Lohman on the open unit ball of an extremally rich JB $^{*}$ -triple $E$ by showing that $\lambda(a)=1/2$ for every non-BP quasi-invertible element $a$ in the open unit ball of $E$ . We also prove that for an extremally rich JB $^{*}$ -triple $E$ , the quadratic conorm $\gamma^{q}(\cdot)$ is continuous at a point $a\in E$ if and only if either $a$ is not von Neumann regular (i.e., $\gamma^{q}(a)=0$ ) or $a$ is Brown–Pedersen quasi-invertible.
</p>projecteuclid.org/euclid.afa/1474652183_20160923133628Fri, 23 Sep 2016 13:36 EDTMaximal Banach ideals of Lipschitz mapshttp://projecteuclid.org/euclid.afa/1474652184<strong>M. G. Cabrera-Padilla</strong>, <strong>J. A. Chávez-Domínguez</strong>, <strong>A. Jiménez-Vargas</strong>, <strong>Moisés Villegas-Vallecillos</strong>. <p><strong>Source: </strong>Annals of Functional Analysis, Volume 7, Number 4, 593--608.</p><p><strong>Abstract:</strong><br/>
There are known results showing a canonical association between Lipschitz cross-norms (norms on the Lipschitz tensor product of a metric space and a Banach space) and ideals of Lipschitz maps from a metric space to a dual Banach space. We extend this association, relating Lipschitz cross-norms to ideals of Lipschitz maps taking values in general Banach spaces. To do that, we prove a Lipschitz version of the representation theorem for maximal operator ideals. As a consequence, we obtain linear characterizations of some ideals of (nonlinear) Lipschitz maps between metric spaces.
</p>projecteuclid.org/euclid.afa/1474652184_20160923133628Fri, 23 Sep 2016 13:36 EDTOn $m$ -generalized invertible operators on Banach spaceshttp://projecteuclid.org/euclid.afa/1474652185<strong>Hamid Ezzahraoui</strong>. <p><strong>Source: </strong>Annals of Functional Analysis, Volume 7, Number 4, 609--621.</p><p><strong>Abstract:</strong><br/>
A bounded linear operator $S$ on a Banach space $X$ is called an $m$ - left generalized inverse of an operator $T$ for a positive integer $m$ if
\[T\sum_{j=0}^{m}(-1)^{j}\binom{m}{j}S^{m-j}T^{m-j}=0,\] and it is called an $m$ - right generalized inverse of $T$ if
\[S\sum_{j=0}^{m}(-1)^{j}\binom{m}{j}T^{m-j}S^{m-j}=0.\] If $T$ is both an $m$ -left and an $m$ -right generalized inverse of $T$ , then it is said to be an $m$ - generalized inverse of $T$ .
This paper has two purposes. The first is to extend the notion of generalized inverse to $m$ -generalized inverse of an operator on Banach spaces and to give some structure results. The second is to generalize some properties of $m$ -partial isometries on Hilbert spaces to the class of $m$ -left generalized invertible operators on Banach spaces. In particular, we study some cases in which a power of an $m$ -left generalized invertible operator is again $m$ -left generalized invertible.
</p>projecteuclid.org/euclid.afa/1474652185_20160923133628Fri, 23 Sep 2016 13:36 EDTOn the Araki–Lieb–Thirring inequality in the semifinite von Neumann algebrahttp://projecteuclid.org/euclid.afa/1474652186<strong>Yazhou Han</strong>. <p><strong>Source: </strong>Annals of Functional Analysis, Volume 7, Number 4, 622--635.</p><p><strong>Abstract:</strong><br/>
This paper extends a recent matrix trace inequality of Bourin–Lee to semifinite von Neumann algebras. This provides a generalization of the Lieb–Thirring-type inequality in von Neumann algebras due to Kosaki. Some new inequalities, even in the matrix case, are also given for the Heinz means.
</p>projecteuclid.org/euclid.afa/1474652186_20160923133628Fri, 23 Sep 2016 13:36 EDTThe BD property in spaces of compact operatorshttp://projecteuclid.org/euclid.afa/1475685110<strong>Ioana Ghenciu</strong>. <p><strong>Source: </strong>Annals of Functional Analysis, Volume 7, Number 4, 636--645.</p><p><strong>Abstract:</strong><br/>
For Banach spaces $X$ and $Y$ , let $K_{w^{*}}(X^{*},Y)$ denote the space of all $w^{*}-w$ continuous compact operators from $X^{*}$ to $Y$ endowed with the operator norm. A Banach space $X$ has the $\mathit{BD}$ property if every limited subset of $X$ is relatively weakly compact. We prove that if $X$ has the Gelfand–Phillips property and $Y$ has the $\mathit{BD}$ property, then $K_{w^{*}}(X^{*},Y)$ has the $\mathit{BD}$ property.
</p>projecteuclid.org/euclid.afa/1475685110_20161005123200Wed, 05 Oct 2016 12:32 EDTDominated operators from lattice-normed spaces to sequence Banach latticeshttp://projecteuclid.org/euclid.afa/1475685111<strong>Nariman Abasov</strong>, <strong>Abd El Monem Megahed</strong>, <strong>Marat Pliev</strong>. <p><strong>Source: </strong>Annals of Functional Analysis, Volume 7, Number 4, 646--655.</p><p><strong>Abstract:</strong><br/>
We show that every dominated linear operator from a Banach–Kantorovich space over an atomless Dedekind-complete vector lattice to a sequence Banach lattice $\ell_{p}(\Gamma)$ or $c_{0}(\Gamma)$ is narrow. As a consequence, we obtain that an atomless Banach lattice cannot have a finite-dimensional decomposition of a certain kind. Finally, we show that the order-narrowness of a linear dominated operator $T$ from a lattice-normed space $V$ to the Banach space with a mixed norm $(W,F)$ over an order-continuous Banach lattice $F$ implies the order-narrowness of its exact dominant | $T$ | .
</p>projecteuclid.org/euclid.afa/1475685111_20161005123200Wed, 05 Oct 2016 12:32 EDTGeometric constants for quantifying the difference between orthogonality typeshttp://projecteuclid.org/euclid.afa/1475685112<strong>Vitor Balestro</strong>, <strong>Horst Martini</strong>, <strong>Ralph Teixeira</strong>. <p><strong>Source: </strong>Annals of Functional Analysis, Volume 7, Number 4, 656--671.</p><p><strong>Abstract:</strong><br/>
This article is devoted to introducing new geometric constants that quantify the difference between Roberts orthogonality and Birkhoff orthogonality in normed planes. We start by characterizing Roberts orthogonality in two different ways: via bisectors of two points and the use of certain linear transformations. Each of these characterizations yields one of those geometric constants that we study.
</p>projecteuclid.org/euclid.afa/1475685112_20161005123200Wed, 05 Oct 2016 12:32 EDTA new characterization of the bounded approximation propertyhttp://projecteuclid.org/euclid.afa/1475685113<strong>Ju Myung Kim</strong>, <strong>Keun Young Lee</strong>. <p><strong>Source: </strong>Annals of Functional Analysis, Volume 7, Number 4, 672--677.</p><p><strong>Abstract:</strong><br/>
We prove that a Banach space $X$ has the bounded approximation property if and only if, for every separable Banach space $Z$ and every injective operator $T$ from $Z$ to $X$ , there exists a net $(S_{\alpha})$ of finite-rank operators from $Z$ to $X$ with $\|S_{\alpha}\|\leq\lambda_{T}$ such that $\lim_{\alpha}\|S_{\alpha}z-Tz\|=0$ for every $z\in Z$ .
</p>projecteuclid.org/euclid.afa/1475685113_20161005123200Wed, 05 Oct 2016 12:32 EDTGateaux derivative of the norm in $\mathcal{K}(X;Y)$http://projecteuclid.org/euclid.afa/1475685114<strong>Paweł Wójcik</strong>. <p><strong>Source: </strong>Annals of Functional Analysis, Volume 7, Number 4, 678--685.</p><p><strong>Abstract:</strong><br/>
In this article, we consider the $\varphi$ -Gateaux derivative of the norm in spaces of compact operators in such a way as to extend the Kečkić theorem. Our main result determines the $\varphi$ -Gateaux derivative of the $\mathcal{K}(X;Y)$ norm.
</p>projecteuclid.org/euclid.afa/1475685114_20161005123200Wed, 05 Oct 2016 12:32 EDTDense Banach subalgebras of the null sequence algebra which do not satisfy a differential seminorm conditionhttp://projecteuclid.org/euclid.afa/1475685115<strong>Larry B. Schweitzer</strong>. <p><strong>Source: </strong>Annals of Functional Analysis, Volume 7, Number 4, 686--690.</p><p><strong>Abstract:</strong><br/>
We construct dense Banach subalgebras $A$ of the null sequence algebra $c_{0}$ which are spectral-invariant but do not satisfy the $D_{1}$ -condition $\Vert ab\Vert _{A}\leq K(\Vert a\Vert _{\infty}\Vertb\Vert _{A}+\Vert a\Vert _{A}\Vert b\Vert _{\infty})$ for all $a,b\in A$ . The sequences in $A$ vanish in a skewed manner with respect to an unbounded function $\sigma\colon{\mathbb{N}}\rightarrow[1,\infty)$ .
</p>projecteuclid.org/euclid.afa/1475685115_20161005123200Wed, 05 Oct 2016 12:32 EDTThe $\lambda ^{+r}(\mu )$ -statistical convergencehttp://projecteuclid.org/euclid.afa/1476450343<strong>B. de Malafosse</strong>, <strong>M. Mursaleen</strong>, <strong>V. Rakočević</strong>. <p><strong>Source: </strong>Annals of Functional Analysis, Volume 8, Number 1, 1--15.</p><p><strong>Abstract:</strong><br/>
Let $\lambda =(\lambda _{n})_{n\geq 1}$ be a nondecreasing sequence of positive numbers tending to infinity such that $\lambda _{1}=1$ and $\lambda_{n+1}\leq \lambda _{n}+1$ for all $n$ , and let $I_{n}=[n-\lambda _{n}+1,n]$ for $n=1,2,\ldots$ . Then for any given nonzero sequence $\mu $ , we define by $\Delta ^{+}(\mu)$ the operator that generalizes the operator of the first difference and is defined by $\Delta ^{+}(\mu )x_{k}=\mu_{k}(x_{k}-x_{k+1})$ . In this article, for any given integer $r\geq 1$ , we deal with the $\lambda ^{+r}(\mu )$ -statistical convergence that generalizes in a certain sense the well-known $\lambda _{E}^{r}$ -statistical convergence. The main results consist in determining sets of sequences $\chi $ and $\chi ^{\prime }$ of the form $s_{\xi }^{0}$ satisfying $\chi \subset [V,\lambda ]_{0}(\Delta ^{+r}(\mu ))\subset \chi^{\prime }$ and sets $\kappa $ and $\kappa^{\prime }$ of the form $s_{\xi }$ satisfying $\kappa \leq [V,\lambda ]_{\infty }(\lambda^{+r}(\mu ))\leq \kappa ^{\prime }$ . This study is justified since the infinite matrix associated with the operator $\Delta ^{+r}(\mu )$ cannot be explicitly calculated for all ${r}$ .
</p>projecteuclid.org/euclid.afa/1476450343_20161014090545Fri, 14 Oct 2016 09:05 EDTCharacterizations and applications of three types of nearly convex pointshttp://projecteuclid.org/euclid.afa/1476450344<strong>Zihou Zhang</strong>, <strong>Yu Zhou</strong>, <strong>Chunyan Liu</strong>. <p><strong>Source: </strong>Annals of Functional Analysis, Volume 8, Number 1, 16--26.</p><p><strong>Abstract:</strong><br/>
By using some geometric properties and nested sequence of balls, we prove seven necessary and sufficient conditions such that a point $x$ in the unit sphere of Banach space $X$ is a nearly rotund point of the unit ball of the bidual space. For any closed convex set $C\subset X$ and $x\in X\setminus C$ with $P_{C}(x)\neq\emptyset$ , we give a series of characterizations such that $C$ is approximatively compact or approximatively weakly compact for $x$ by using three types of nearly convex points. Furthermore, making use of an S point, we present a characterization such that the convex subset $C$ is approximatively compact for some $x$ in $X\setminus C$ . We also establish a relationship between nested sequence of balls and the approximate compactness of the closed convex subset $C$ for some $x\in X\setminus C$ .
</p>projecteuclid.org/euclid.afa/1476450344_20161014090545Fri, 14 Oct 2016 09:05 EDTCone isomorphisms and expressions of some completely positive mapshttp://projecteuclid.org/euclid.afa/1476450345<strong>Xiuhong Sun</strong>, <strong>Yuan Li</strong>. <p><strong>Source: </strong>Annals of Functional Analysis, Volume 8, Number 1, 27--37.</p><p><strong>Abstract:</strong><br/>
Let $B{\mathcal{(H)}}$ , $K{\mathcal{(H)}}$ and $T{\mathcal{(H)}}$ be the set of all bounded linear operators, compact operators, and trace-class operators on the Hilbert space $\mathcal{H}$ . The cone of all completely positive maps from $K{\mathcal{(H)}}$ into $T{\mathcal{(K)}}$ and all normal completely positive maps from $B{\mathcal{(K)}}$ into $T{\mathcal{(H)}}$ is denoted by $\mathit{CP}(K{\mathcal{(H)}},T{\mathcal{(K)}})$ and $\mathit{NCP}(B{\mathcal{(K)}},T{\mathcal{(H)}})$ , respectively. In this note, the order structures of the positive cones $\mathit{CP}(K{\mathcal{(H)}},T{\mathcal{(K)}})$ and $\mathit{NCP}(B{\mathcal{(K)}},T{\mathcal{(H)}})$ are investigated. First, we show that $\mathit{CP}(K{\mathcal{(H)}},T{\mathcal{(K)}})$ , $\mathit{NCP}(B{\mathcal{(K)}},T{\mathcal{(H)}})$ , and $T{\mathcal{(K\otimesH)}}^{+}$ are cone-isomorphic. Then we give the operator sum representation for the map $\Phi\in\mathit{CP}(K{\mathcal{(H)}},T{\mathcal{(K)}})$ .
</p>projecteuclid.org/euclid.afa/1476450345_20161014090545Fri, 14 Oct 2016 09:05 EDT$(p,\sigma)$ -Absolutely Lipschitz operatorshttp://projecteuclid.org/euclid.afa/1477918633<strong>D. Achour</strong>, <strong>P. Rueda</strong>, <strong>R. Yahi</strong>. <p><strong>Source: </strong>Annals of Functional Analysis, Volume 8, Number 1, 38--50.</p><p><strong>Abstract:</strong><br/>
Due to recent advances in the theory of ideals of Lipschitz mappings, we introduce $(p,\sigma)$ -absolutely Lipschitz mappings as an interpolating class between Lipschitz mappings and Lipschitz absolutely $p$ -summing mappings. Among other results, we prove a factorization theorem that provides a reformulation to the one given by Farmer and Johnson for Lipschitz absolutely $p$ -summing mappings.
</p>projecteuclid.org/euclid.afa/1477918633_20161031085722Mon, 31 Oct 2016 08:57 EDTGeometric description of multiplier modules for Hilbert $C^{*}$ -modules in simple caseshttp://projecteuclid.org/euclid.afa/1477918634<strong>Zhu Jingming</strong>. <p><strong>Source: </strong>Annals of Functional Analysis, Volume 8, Number 1, 51--62.</p><p><strong>Abstract:</strong><br/>
In this article we suggest a vector bundle description for multiplier modules of vector bundles over noncompact spaces. We prove that the isomorphism classes of multiplier modules are dependent on the isomorphism classes of their underlying modules. This gives a way to evaluate the set of extensions of Hilbert modules in topological terms in simple cases.
</p>projecteuclid.org/euclid.afa/1477918634_20161031085722Mon, 31 Oct 2016 08:57 EDTSimilarity orbits of complex symmetric operatorshttp://projecteuclid.org/euclid.afa/1477918635<strong>Sen Zhu</strong>, <strong>Jiayin Zhao</strong>. <p><strong>Source: </strong>Annals of Functional Analysis, Volume 8, Number 1, 63--74.</p><p><strong>Abstract:</strong><br/>
An operator $T$ on a complex Hilbert space $\mathcal{H}$ is said to be complex symmetric if $T$ can be represented as a symmetric matrix relative to some orthonormal basis for $\mathcal{H}$ . In this article we explore the stability of complex symmetry under the condition of similarity. It is proved that the similarity orbit of an operator $T$ is included in the class of complex symmetric operators if and only if $T$ is an algebraic operator of degree at most $2$ .
</p>projecteuclid.org/euclid.afa/1477918635_20161031085722Mon, 31 Oct 2016 08:57 EDT$\varphi$ -contractibility and character contractibility of Fréchet algebrashttp://projecteuclid.org/euclid.afa/1477918636<strong>Fatemeh Abtahi</strong>, <strong>Somaye Rahnama</strong>. <p><strong>Source: </strong>Annals of Functional Analysis, Volume 8, Number 1, 75--89.</p><p><strong>Abstract:</strong><br/>
Right $\varphi$ -contractibility and right character contractibility of Banach algebras have been introduced and investigated. Here, we introduce and generalize these concepts for Fréchet algebras. We then verify available results about right $\varphi$ -contractibility and right character contractibility of Banach algebras for Fréchet algebras. Moreover, we provide related results about Segal–Fréchet algebras.
</p>projecteuclid.org/euclid.afa/1477918636_20161031085722Mon, 31 Oct 2016 08:57 EDTThe generalized Drazin inverse of the sum in a Banach algebrahttp://projecteuclid.org/euclid.afa/1477918637<strong>Dijana Mosić</strong>, <strong>Honglin Zou</strong>, <strong>Jianlong Chen</strong>. <p><strong>Source: </strong>Annals of Functional Analysis, Volume 8, Number 1, 90--105.</p><p><strong>Abstract:</strong><br/>
In this article, we obtain new additive results on the generalized Drazin inverse of a sum of two elements in a Banach algebra. Applying these additive results, we also give explicit formulas for the generalized Drazin inverse of a block matrix in a Banach algebra.
</p>projecteuclid.org/euclid.afa/1477918637_20161031085722Mon, 31 Oct 2016 08:57 EDTBaskakov–Szász-type operators based on inverse Pólya–Eggenberger distributionhttp://projecteuclid.org/euclid.afa/1477918638<strong>Arun Kajla</strong>, <strong>Ana Maria Acu</strong>, <strong>P. N. Agrawal</strong>. <p><strong>Source: </strong>Annals of Functional Analysis, Volume 8, Number 1, 106--123.</p><p><strong>Abstract:</strong><br/>
The present article deals with the modified forms of the Baskakov and Szász basis functions. We introduce a Durrmeyer-type operator having the basis functions in summation and integration due to Stancu (1970) and Pǎltǎnea (2008). We obtain some approximation results, which include the Voronovskaja-type asymptotic formula, local approximation, error estimation in terms of the modulus of continuity, and weighted approximation. Also, the rate of convergence for functions with derivatives of bounded variation is established. Furthermore, the convergence of these operators to certain functions is shown by illustrative graphics using MAPLE algorithms.
</p>projecteuclid.org/euclid.afa/1477918638_20161031085722Mon, 31 Oct 2016 08:57 EDTA Grüss type operator inequalityhttp://projecteuclid.org/euclid.afa/1478919626<strong>T. Bottazzi</strong>, <strong>C. Conde</strong>. <p><strong>Source: </strong>Annals of Functional Analysis, Volume 8, Number 1, 124--132.</p><p><strong>Abstract:</strong><br/>
In 2001, Renaud obtained a Grüss type operator inequality involving the usual trace functional. In this article, we give a refinement of that result, and we answer positively Renaud’s open problem.
</p>projecteuclid.org/euclid.afa/1478919626_20161111220043Fri, 11 Nov 2016 22:00 ESTHyperrigid operator systems and Hilbert moduleshttp://projecteuclid.org/euclid.afa/1478919627<strong>P. Shankar</strong>, <strong>A. K. Vijayarajan</strong>. <p><strong>Source: </strong>Annals of Functional Analysis, Volume 8, Number 1, 133--141.</p><p><strong>Abstract:</strong><br/>
It is shown that, for an operator algebra $A$ , the operator system $S=A+A^{*}$ in the $C^{*}$ -algebra $C^{*}(S)$ , and any representation $\rho$ of $C^{*}(S)$ on a Hilbert space $\mathcal{H}$ , the restriction $\rho_{|_{S}}$ has a unique extension property if and only if the Hilbert module $\mathcal{H}$ over $A$ is both orthogonally projective and orthogonally injective. As a corollary we deduce that, when $S$ is separable, the hyperrigidity of $S$ is equivalent to the Hilbert modules over $A$ being both orthogonally projective and orthogonally injective.
</p>projecteuclid.org/euclid.afa/1478919627_20161111220043Fri, 11 Nov 2016 22:00 ESTAn Inequality for expectation of means of positive random variableshttp://projecteuclid.org/euclid.afa/1478919628<strong>Paolo Gibilisco</strong>, <strong>Frank Hansen</strong>. <p><strong>Source: </strong>Annals of Functional Analysis, Volume 8, Number 1, 142--151.</p><p><strong>Abstract:</strong><br/>
Suppose that $X$ , $Y$ are positive random variables and $m$ is a numerical (commutative) mean. We prove that the inequality $\mathrm{E}(m(X,Y))\leqm(\mathrm{E}(X),\mathrm{E}(Y))$ holds if and only if the mean is generated by a concave function. With due changes we also prove that the same inequality holds for all operator means in the Kubo–Ando setting. The case of the harmonic mean was proved by C. R. Rao and B. L. S. Prakasa Rao.
</p>projecteuclid.org/euclid.afa/1478919628_20161111220043Fri, 11 Nov 2016 22:00 ESTComputation of Riemann matrices for the hyperbolic curves of determinantal polynomialshttp://projecteuclid.org/euclid.afa/1484363067<strong>Mao-Ting Chien</strong>, <strong>Hiroshi Nakazato</strong>. <p><strong>Source: </strong>Annals of Functional Analysis, Volume 8, Number 2, 152--167.</p><p><strong>Abstract:</strong><br/>
The numerical range of a matrix, according to Kippenhahn, is determined by a hyperbolic determinantal form of linear Hermitian matrices associated to the matrix. On the other hand, using Riemann theta functions, Helton and Vinnikov confirmed that a hyperbolic form always admits a determinantal representation of linear real symmetric matrices. The Riemann matrix of the hyperbolic curve plays the main role in the existence of real symmetric matrices. In this article, we implement computations of the Riemann matrix and the Abel–Jacobi variety of the hyperbolic curve associated to a determinantal polynomial of a matrix. Further, we prove that the lattice of the Abel–Jacobi variety is decomposed into the direct sum of two orthogonal lattices for some $4\times4$ Toeplitz matrices.
</p>projecteuclid.org/euclid.afa/1484363067_20170116040024Mon, 16 Jan 2017 04:00 ESTPerspectives and completely positive mapshttp://projecteuclid.org/euclid.afa/1484363068<strong>Frank Hansen</strong>. <p><strong>Source: </strong>Annals of Functional Analysis, Volume 8, Number 2, 168--176.</p><p><strong>Abstract:</strong><br/>
We study the filtering of the perspective of a regular operator map of several variables through a completely positive linear map. By this method we are able to extend known operator inequalities of two variables to several variables, with applications in the theory of operator means of several variables. We also extend Lieb and Ruskai’s convexity theorem from two to $n+1$ operator variables for any natural number $n$ .
</p>projecteuclid.org/euclid.afa/1484363068_20170116040024Mon, 16 Jan 2017 04:00 ESTGeneralized shift-invariant systems and approximately dual frameshttp://projecteuclid.org/euclid.afa/1484363069<strong>Ana Benavente</strong>, <strong>Ole Christensen</strong>, <strong>María I. Zakowicz</strong>. <p><strong>Source: </strong>Annals of Functional Analysis, Volume 8, Number 2, 177--189.</p><p><strong>Abstract:</strong><br/>
Dual pairs of frames yield a procedure for obtaining perfect reconstruction of elements in the underlying Hilbert space in terms of superpositions of the frame elements. However, practical constraints often force us to apply sequences that do not exactly form dual frames. In this article, we consider the important case of generalized shift-invariant systems and provide various ways of estimating the deviation from perfect reconstruction that occur when the systems do not form dual frames. The deviation from being dual frames will be measured either in terms of a perturbation condition or in terms of the deviation from equality in the duality conditions.
</p>projecteuclid.org/euclid.afa/1484363069_20170116040024Mon, 16 Jan 2017 04:00 ESTA note on Weyl-type theorems and restrictionshttp://projecteuclid.org/euclid.afa/1485572480<strong>Lihong Chen</strong>, <strong>Weigang Su</strong>. <p><strong>Source: </strong>Annals of Functional Analysis, Volume 8, Number 2, 190--198.</p><p><strong>Abstract:</strong><br/>
Let $X$ be a Banach space, let $T\in L(X)$ be a bounded linear operator, and let $T_{n}$ be a restriction of $T$ on $R(T^{n})$ . This article should be viewed as a note on the research work of Carpintero et al. We give here several different proofs for completeness, and we show the relations of $T$ and $T_{n}$ to a much greater extent. Moreover, we give sufficient conditions for which Weyl-type theorems for $T$ are equivalent to Weyl-type theorems for $T_{n}$ .
</p>projecteuclid.org/euclid.afa/1485572480_20170127220126Fri, 27 Jan 2017 22:01 ESTWeighted backward shift operators with invariant distributionally scrambled subsetshttp://projecteuclid.org/euclid.afa/1485831762<strong>Xinxing Wu</strong>, <strong>Lidong Wang</strong>, <strong>Guanrong Chen</strong>. <p><strong>Source: </strong>Annals of Functional Analysis, Volume 8, Number 2, 199--210.</p><p><strong>Abstract:</strong><br/>
We obtain a sufficient condition to ensure that weighted backward shift operators on Köthe sequence spaces $\lambda_{p}(A)$ admit an invariant distributionally $\varepsilon$ -scrambled subset for any $0\lt \varepsilon\lt \operatorname{diam}\lambda_{p}(A)$ . In particular, every Devaney chaotic weighted backward shift operator on $\lambda_{p}(A)$ supports such a subset.
</p>projecteuclid.org/euclid.afa/1485831762_20170130220247Mon, 30 Jan 2017 22:02 ESTNonsimplicity of certain universal ${\mathrm{C}}^{\ast}$ -algebrashttp://projecteuclid.org/euclid.afa/1485831763<strong>Marcel de Jeu</strong>, <strong>Rachid El Harti</strong>, <strong>Paulo R. Pinto</strong>. <p><strong>Source: </strong>Annals of Functional Analysis, Volume 8, Number 2, 211--214.</p><p><strong>Abstract:</strong><br/>
Given $n\geq2$ , $z_{ij}\in\mathbb{T}$ such that $z_{ij}=\overline{z}_{ji}$ for $1\leq i,j\leq n$ and $z_{ii}=1$ for $1\leq i\leq n$ , and integers $p_{1},\ldots,p_{n}\geq1$ , we show that the universal ${\mathrm{C}}^{\ast}$ -algebra generated by unitaries $u_{1},\ldots,u_{n}$ such that $u_{i}^{p_{i}}u_{j}^{p_{j}}=z_{ij}u_{j}^{p_{j}}u_{i}^{p_{i}}$ for $1\leq i,j\leq n$ is not simple if at least one exponent $p_{i}$ is at least two. We indicate how the method of proof by “working with various quotients” can be used to establish nonsimplicity of universal ${\mathrm{C}}^{\ast}$ -algebras in other cases.
</p>projecteuclid.org/euclid.afa/1485831763_20170130220247Mon, 30 Jan 2017 22:02 ESTGeometric constants of $\pi/2$ -rotation invariant norms on $\mathbb{R}^{2}$http://projecteuclid.org/euclid.afa/1485831764<strong>Yukino Tomizawa</strong>, <strong>Ken-Ichi Mitani</strong>, <strong>Kichi-Suke Saito</strong>, <strong>Ryotaro Tanaka</strong>. <p><strong>Source: </strong>Annals of Functional Analysis, Volume 8, Number 2, 215--230.</p><p><strong>Abstract:</strong><br/>
In this article, we study the (modified) von Neumann–Jordan constant and Zbăganu constant of $\pi/2$ -rotation invariant norms on $\mathbb{R}^{2}$ . Some estimations of these geometric constants are given. As an application, we construct various examples consisting of $\pi/2$ -rotation invariant norms.
</p>projecteuclid.org/euclid.afa/1485831764_20170130220247Mon, 30 Jan 2017 22:02 EST$L^{p}$ -Inequalities and Parseval-type relations for the Mehler–Fock transform of general orderhttp://projecteuclid.org/euclid.afa/1485918116<strong>Benito J. González</strong>, <strong>Emilio R. Negrín</strong>. <p><strong>Source: </strong>Annals of Functional Analysis, Volume 8, Number 2, 231--239.</p><p><strong>Abstract:</strong><br/>
In this article we study new $L^{p}$ -boundedness properties for the Mehler–Fock transform of general order on the spaces $L^{p}((0,\infty),e^{\alpha x}dx)$ and $L^{p}((0,\infty),(1+x)^{\gamma}dx)$ , $1\leq p\leq\infty$ , and $\alpha,\gamma\in\mathbb{R}$ . We also obtain Parseval-type relations over these spaces.
</p>projecteuclid.org/euclid.afa/1485918116_20170131220214Tue, 31 Jan 2017 22:02 ESTSome operator inequalities for unitarily invariant normshttp://projecteuclid.org/euclid.afa/1485918117<strong>Jianguo Zhao</strong>, <strong>Junliang Wu</strong>. <p><strong>Source: </strong>Annals of Functional Analysis, Volume 8, Number 2, 240--247.</p><p><strong>Abstract:</strong><br/>
This note aims to present some operator inequalities for unitarily invariant norms. First, a Zhan-type inequality for unitarily invariant norms is given. Moreover, some operator inequalities for the Cauchy–Schwarz type are also established.
</p>projecteuclid.org/euclid.afa/1485918117_20170131220214Tue, 31 Jan 2017 22:02 ESTTriple solutions for quasilinear one-dimensional $p$ -Laplacian elliptic equations in the whole spacehttp://projecteuclid.org/euclid.afa/1488358820<strong>Gabriele Bonanno</strong>, <strong>Donal O’Regan</strong>, <strong>Francesca Vetro</strong>. <p><strong>Source: </strong>Annals of Functional Analysis, Volume 8, Number 2, 248--258.</p><p><strong>Abstract:</strong><br/>
In this paper, we establish the existence of three possibly nontrivial solutions for a Dirichlet problem on the real line without assuming on the nonlinearity asymptotic conditions at infinity. As a particular case, when the nonlinearity is superlinear at zero and sublinear at infinity, the existence of two nontrivial solutions is obtained. This approach is based on variational methods and, more precisely, a critical points theorem, which assumes a more general condition than the classical Palais–Smale condition, is exploited.
</p>projecteuclid.org/euclid.afa/1488358820_20170301040047Wed, 01 Mar 2017 04:00 ESTHadamard gap series in weighted-type spaces on the unit ballhttp://projecteuclid.org/euclid.afa/1488358821<strong>Bingyang Hu</strong>, <strong>Songxiao Li</strong>. <p><strong>Source: </strong>Annals of Functional Analysis, Volume 8, Number 2, 259--269.</p><p><strong>Abstract:</strong><br/>
We give a sufficient and necessary condition for an analytic function $f(z)$ on the unit ball $\mathbb{B}$ in $\mathbb{C}^{n}$ with Hadamard gaps, that is, for $f(z)=\sum_{k=1}^{\infty}P_{n_{k}}(z)$ where $P_{n_{k}}(z)$ is a homogeneous polynomial of degree $n_{k}$ and $n_{k+1}/n_{k}\ge c\gt 1$ for all $k\in\mathbb{N}$ , to belong to the weighted-type space $H^{\infty}_{\mu}$ and the corresponding little weighted-type space $H^{\infty}_{\mu,0}$ under some condition posed on the weighted funtion $\mu$ . We also study the growth rate of those functions in $H^{\infty}_{\mu}$ .
</p>projecteuclid.org/euclid.afa/1488358821_20170301040047Wed, 01 Mar 2017 04:00 ESTLocal Lie derivations on certain operator algebrashttp://projecteuclid.org/euclid.afa/1488358822<strong>Dan Liu</strong>, <strong>Jianhua Zhang</strong>. <p><strong>Source: </strong>Annals of Functional Analysis, Volume 8, Number 2, 270--280.</p><p><strong>Abstract:</strong><br/>
In this paper, we investigate local Lie derivations of a certain class of operator algebras and show that, under certain conditions, every local Lie derivation of such an algebra is a Lie derivation.
</p>projecteuclid.org/euclid.afa/1488358822_20170301040047Wed, 01 Mar 2017 04:00 ESTGreen’s theorem for crossed products by Hilbert $C^{*}$ -bimoduleshttp://projecteuclid.org/euclid.afa/1491280437<strong>Mauricio Achigar</strong>. <p><strong>Source: </strong>Annals of Functional Analysis, Volume 8, Number 3, 281--290.</p><p><strong>Abstract:</strong><br/>
Green’s theorem gives a Morita equivalence $C_{0}(G/H,A)\rtimes G\simA\rtimes H$ for a closed subgroup $H$ of a locally compact group $G$ acting on a $C^{*}$ -algebra $A$ . We prove an analogue of Green’s theorem in the case $G=\mathbb{Z}$ , where the automorphism generating the action is replaced by a Hilbert $C^{*}$ -bimodule.
</p>projecteuclid.org/euclid.afa/1491280437_20170720220234Thu, 20 Jul 2017 22:02 EDTCharacterizations of Lipschitz space via commutators of some bilinear integral operatorshttp://projecteuclid.org/euclid.afa/1491280438<strong>Juan Zhang</strong>, <strong>Zongguang Liu</strong>. <p><strong>Source: </strong>Annals of Functional Analysis, Volume 8, Number 3, 291--302.</p><p><strong>Abstract:</strong><br/>
In this article, we give some characterizations of Lipschitz space via commutators of bilinear singular integral operators and bilinear fractional integral operators, respectively.
</p>projecteuclid.org/euclid.afa/1491280438_20170720220234Thu, 20 Jul 2017 22:02 EDTRate of approximation by $q$ -Durrmeyer operators in $L_{p}([0,1])$ , $1\leq p\leq\infty$http://projecteuclid.org/euclid.afa/1491280439<strong>Asha Ram Gairola</strong>, <strong>Karunesh Kumar Singh</strong>, <strong>Vishnu Narayan Mishra</strong>. <p><strong>Source: </strong>Annals of Functional Analysis, Volume 8, Number 3, 303--313.</p><p><strong>Abstract:</strong><br/>
We obtain global rates of approximation by $q$ -Durrmeyer operators $D_{n,q}(f;x)$ for the functions in the class $L_{p}([0,1]),1\leq p\leq \infty$ . First, rates of approximation in terms of the norms of $f$ and $f'$ and in terms of the ordinary modulus of smoothness are obtained. Subsequently, we obtain rates of approximation in terms of the generalized modulus of smoothness $\omega_{\varphi}(f,\delta)$ .
</p>projecteuclid.org/euclid.afa/1491280439_20170720220234Thu, 20 Jul 2017 22:02 EDTLevel sets of the condition spectrumhttp://projecteuclid.org/euclid.afa/1491280440<strong>D. Sukumar</strong>, <strong>S. Veeramani</strong>. <p><strong>Source: </strong>Annals of Functional Analysis, Volume 8, Number 3, 314--328.</p><p><strong>Abstract:</strong><br/>
For $0\lt \epsilon\leq1$ and an element $a$ of a complex unital Banach algebra $\mathcal{A}$ , we prove the following two topological properties about the level sets of the condition spectrum. (1) If $\epsilon=1$ , then the $1$ -level set of the condition spectrum of $a$ has an empty interior unless $a$ is a scalar multiple of the unity. (2) If $0\lt \epsilon\lt 1$ , then the $\epsilon$ -level set of the condition spectrum of $a$ has an empty interior in the unbounded component of the resolvent set of $a$ . Further, we show that, if the Banach space $X$ is complex uniformly convex or if $X^{*}$ is complex uniformly convex, then, for any operator $T$ acting on $X$ , the level set of the $\epsilon$ -condition spectrum of $T$ has an empty interior.
</p>projecteuclid.org/euclid.afa/1491280440_20170720220234Thu, 20 Jul 2017 22:02 EDTStability of functional equations arising from number theory and determinant of matriceshttp://projecteuclid.org/euclid.afa/1491280441<strong>Chang-Kwon Choi</strong>, <strong>Jaeyoung Chung</strong>, <strong>Thomas Riedel</strong>, <strong>Prasanna K. Sahoo</strong>. <p><strong>Source: </strong>Annals of Functional Analysis, Volume 8, Number 3, 329--340.</p><p><strong>Abstract:</strong><br/>
In this paper, we consider the Ulam–Hyers stability of the functional equations \[f(ux-vy,uy-vx)=f(x,y)f(u,v),\] \[f(ux+vy,uy-vx)=f(x,y)f(u,v),\] \[f(ux+vy,uy+vx)=f(x,y)f(u,v),\] \[f(ux-vy,uy+vx)=f(x,y)f(u,v)\] for all $x,y,u,v\in\Bbb{R}$ , where $f:\Bbb{R}^{2}\to\Bbb{R}$ , which arise from number theory and are connected with the characterizations of the determinant and permanent of two-by-two matrices.
</p>projecteuclid.org/euclid.afa/1491280441_20170720220234Thu, 20 Jul 2017 22:02 EDTOn the weak convergence theorem for nonexpansive semigroups in Banach spaceshttp://projecteuclid.org/euclid.afa/1492826604<strong>Rongjie Yao</strong>, <strong>Liping Yang</strong>. <p><strong>Source: </strong>Annals of Functional Analysis, Volume 8, Number 3, 341--349.</p><p><strong>Abstract:</strong><br/>
Assume that $K$ is a closed convex subset of a uniformly convex Banach space $E$ , and assume that $\{T(s)\}_{s\gt 0}$ is a nonexpansive semigroup on $K$ . By using the following implicit iteration sequence $\{x_{n}\}$ defined by \[x_{n}=(1-\alpha_{n})x_{n-1}+\alpha_{n}\cdot\frac{1}{t_{n}}\int _{0}^{t_{n}}T(s)x_{n}\,ds,\quad\forall n\geq1,\] the main purpose of this paper is to establish a weak convergence theorem for the nonexpansive semigroup $\{T(s)\}_{s\gt 0}$ in uniformly convex Banach spaces without the Opial property. Our results are different from some recently announced results.
</p>projecteuclid.org/euclid.afa/1492826604_20170720220234Thu, 20 Jul 2017 22:02 EDTNew moduli for Banach spaceshttp://projecteuclid.org/euclid.afa/1492826601<strong>G. Ivanov</strong>, <strong>H. Martini</strong>. <p><strong>Source: </strong>Annals of Functional Analysis, Volume 8, Number 3, 350--365.</p><p><strong>Abstract:</strong><br/>
Modifying the moduli of supporting convexity and supporting smoothness, we introduce new moduli for Banach spaces which occur, for example, as lengths of catheti of right-angled triangles (defined via so-called quasiorthogonality ). These triangles have two boundary points of the unit ball of a Banach space as endpoints of their hypotenuse, and their third vertex lies in a supporting hyperplane of one of the two other vertices. Among other things, it is our goal to quantify via such triangles the local deviation of the unit sphere from its supporting hyperplanes. We prove respective Day–Nordlander-type results involving generalizations of the modulus of convexity and the modulus of Banaś.
</p>projecteuclid.org/euclid.afa/1492826601_20170720220234Thu, 20 Jul 2017 22:02 EDTThe commutant of a multiplication operator with a finite Blaschke product symbol on the Sobolev disk algebrahttp://projecteuclid.org/euclid.afa/1492826603<strong>Ruifang Zhao</strong>, <strong>Zongyao Wang</strong>, <strong>David R. Larson</strong>. <p><strong>Source: </strong>Annals of Functional Analysis, Volume 8, Number 3, 366--376.</p><p><strong>Abstract:</strong><br/>
Let $R(\mathbb{D})$ be the algebra generated in the Sobolev space $W^{22}(\mathbb{D})$ by the rational functions with poles outside the unit disk $\overline{\mathbb{D}}$ . This is called the Sobolev disk algebra . In this article, the commutant of the multiplication operator $M_{B(z)}$ on $R(\mathbb{D})$ is studied, where $B(z)$ is an n-Blaschke product. We prove that an operator $A\in\mathcal{L}(R(\mathbb{D}))$ is in $\mathcal{A}'(M_{B(z)})$ if and only if $A=\sum_{i=1}^{n}M_{h_{i}}M_{\Delta(z)}^{-1}T_{i}$ , where $\{h_{i}\}_{i=1}^{n}\subset R(\mathbb{D})$ , and $T_{i}\in\mathcal{L}(R(\mathbb{D}))$ is given by $(T_{i}g)(z)=\sum_{j=1}^{n}(-1)^{i+j}\Delta_{ij}(z)g(G_{j-1}(z))$ , $i=1,2,\ldots,n$ , $G_{0}(z)\equiv z$ .
</p>projecteuclid.org/euclid.afa/1492826603_20170720220234Thu, 20 Jul 2017 22:02 EDTOn a conjecture of the norm Schwarz inequalityhttp://projecteuclid.org/euclid.afa/1492826602<strong>Tomohiro Hayashi</strong>. <p><strong>Source: </strong>Annals of Functional Analysis, Volume 8, Number 3, 377--385.</p><p><strong>Abstract:</strong><br/>
Let $A$ be a positive invertible matrix, and let $B$ be a normal matrix. Following the investigation of Ando, we show that $\Vert A\sharp(B^{*}A^{-1}B)\Vert\geq\Vert B\Vert$ , where $\sharp$ denotes the geometric mean, fails in general.
</p>projecteuclid.org/euclid.afa/1492826602_20170720220234Thu, 20 Jul 2017 22:02 EDTOn certain properties of Cuntz–Krieger-type algebrashttp://projecteuclid.org/euclid.afa/1494295270<strong>Bernhard Burgstaller</strong>, <strong>D. Gwion Evans</strong>. <p><strong>Source: </strong>Annals of Functional Analysis, Volume 8, Number 3, 386--397.</p><p><strong>Abstract:</strong><br/>
This note presents a further study of the class of Cuntz–Krieger-type algebras. A necessary and sufficient condition is identified that ensures that the algebra is purely infinite, the ideal structure is studied, and nuclearity is proved by presenting the algebra as a crossed product of an AF-algebra by an abelian group. The results are applied to examples of Cuntz–Krieger-type algebras, such as higher-rank semigraph $C^{*}$ -algebras and higher-rank Exel–Laca algebras.
</p>projecteuclid.org/euclid.afa/1494295270_20170720220234Thu, 20 Jul 2017 22:02 EDTStability of the Lyapunov exponents under perturbationshttp://projecteuclid.org/euclid.afa/1494900338<strong>Luis Barreira</strong>, <strong>Claudia Valls</strong>. <p><strong>Source: </strong>Annals of Functional Analysis, Volume 8, Number 3, 398--410.</p><p><strong>Abstract:</strong><br/>
For a linear-delay equation on an arbitrary Banach space, we describe a condition so that the Lyapunov exponents of the equation persist under sufficiently small linear as well as nonlinear perturbations. We consider both cases of discrete and continuous time with the study of delay-difference equations and delay equations, respectively. The delay can be any number from zero to infinity.
</p>projecteuclid.org/euclid.afa/1494900338_20170720220234Thu, 20 Jul 2017 22:02 EDTFunctional equations on double coset hypergroupshttp://projecteuclid.org/euclid.afa/1494640815<strong>Żywilla Fechner</strong>, <strong>László Székelyhidi</strong>. <p><strong>Source: </strong>Annals of Functional Analysis, Volume 8, Number 3, 411--423.</p><p><strong>Abstract:</strong><br/>
In this paper we describe the complex-valued solutions defined on a double coset hypergroup of the exponential, additive, and quadratic functional equations. Moreover, the $m$ -sine functions on a double coset hypergroup are discussed. The double coset hypergroup we consider is closely related to affine groups and spherical functions on them.
</p>projecteuclid.org/euclid.afa/1494640815_20170720220234Thu, 20 Jul 2017 22:02 EDTSherman type theorem on $C^{\ast}$ -algebrashttps://projecteuclid.org/euclid.afa/1494640814<strong>Marek Niezgoda</strong>. <p><strong>Source: </strong>Annals of Functional Analysis, Volume 8, Number 4, 425--434.</p><p><strong>Abstract:</strong><br/>
In this paper, a new definition of majorization for $C^{\ast}$ -algebras is introduced. Sherman’s inequality is extended to self-adjoint operators and positive linear maps by applying the method of premajorization used for comparing two tuples of objects. A general result in a matrix setting is established. Special cases of the main theorem are studied. In particular, a HLPK-type inequality is derived.
</p>projecteuclid.org/euclid.afa/1494640814_20171026220223Thu, 26 Oct 2017 22:02 EDTEquivalent results to Banach’s contraction principlehttps://projecteuclid.org/euclid.afa/1495505153<strong>Maher Berzig</strong>, <strong>Cristina-Olimpia Rus</strong>, <strong>Mircea-Dan Rus</strong>. <p><strong>Source: </strong>Annals of Functional Analysis, Volume 8, Number 4, 435--445.</p><p><strong>Abstract:</strong><br/>
We present two versions of the well-known Banach contraction principle: one in the context of extended metric spaces for which the distance mapping is allowed to be infinite, the other in the context of metric spaces endowed with a compatible binary relation. We also point out that these two results and the Banach contraction principle are actually equivalent.
</p>projecteuclid.org/euclid.afa/1495505153_20171026220223Thu, 26 Oct 2017 22:02 EDTChlodowsky–Szasz–Appell-type operators for functions of two variableshttps://projecteuclid.org/euclid.afa/1495677675<strong>Manjari Sidharth</strong>, <strong>Ana Maria Acu</strong>, <strong>P. N. Agrawal</strong>. <p><strong>Source: </strong>Annals of Functional Analysis, Volume 8, Number 4, 446--459.</p><p><strong>Abstract:</strong><br/>
This article deals with the approximation properties of the bivariate operators which are the combination of Bernstein–Chlodowsky operators and the Szász operators involving Appell polynomials. We investigate the degree of approximation of the operators with the help of the complete modulus of continuity and the partial moduli of continuity. In the last section of the paper, we introduce the generalized Boolean sum (GBS) of these bivariate Chlodowsky–Szasz–Appell-type operators and examine the order of approximation in the Bögel space of continuous functions by means of the mixed modulus of smoothness.
</p>projecteuclid.org/euclid.afa/1495677675_20171026220223Thu, 26 Oct 2017 22:02 EDTNonlinear isometries between function spaceshttps://projecteuclid.org/euclid.afa/1496368961<strong>Kathleen Roberts</strong>, <strong>Kristopher Lee</strong>. <p><strong>Source: </strong>Annals of Functional Analysis, Volume 8, Number 4, 460--472.</p><p><strong>Abstract:</strong><br/>
We demonstrate that any surjective isometry $T\colon \mathcal{A}\to \mathcal{B}$ not assumed to be linear between unital, completely regular subspaces of complex-valued, continuous functions on compact Hausdorff spaces is of the form \begin{equation*}T(f)=T(0)+\operatorname{Re}[\mu \cdot(f\circ\tau)]+i\operatorname{Im}[\nu \cdot(f\circ\rho)],\end{equation*} where $\mu$ and $\nu$ are continuous and unimodular, there exists a clopen set $K$ with $\nu=\mu$ on $K$ and $\nu=-\mu$ on $K^{c}$ , and $\tau$ and $\rho$ are homeomorphisms.
</p>projecteuclid.org/euclid.afa/1496368961_20171026220223Thu, 26 Oct 2017 22:02 EDTSemifinite tracial subalgebrashttps://projecteuclid.org/euclid.afa/1496368960<strong>Turdebek N. Bekjan</strong>, <strong>Azhar Oshanova</strong>. <p><strong>Source: </strong>Annals of Functional Analysis, Volume 8, Number 4, 473--478.</p><p><strong>Abstract:</strong><br/>
Let ${\mathcal{M}}$ be a semifinite von Neumann algebra, and let ${\mathcal{A}}$ be a tracial subalgebra of $\mathcal{M}$ . We show that ${\mathcal{A}}$ is a subdiagonal algebra of ${\mathcal{M}}$ if and only if it has the unique normal state extension property and is a $\tau$ -maximal tracial subalgebra, which is also equivalent to ${\mathcal{A}}$ having the unique normal state extension property and satisfying $L_{2}$ -density.
</p>projecteuclid.org/euclid.afa/1496368960_20171026220223Thu, 26 Oct 2017 22:02 EDTOn Fredholm completions of partial operator matriceshttps://projecteuclid.org/euclid.afa/1496368962<strong>Guojun Hai</strong>, <strong>Nan Zhang</strong>. <p><strong>Source: </strong>Annals of Functional Analysis, Volume 8, Number 4, 479--489.</p><p><strong>Abstract:</strong><br/>
The aim of this article is to study the Fredholm completion problem of two-by-two partial operator matrices in which the lower-left entry is unspecified and others are specified. By using the methods of operator matrix representation and operator equation, we obtain necessity and sufficiency conditions for the partial operator matrices to have a Fredholm completion with the property that the lower-right entry of its Fredholm inverses is specified.
</p>projecteuclid.org/euclid.afa/1496368962_20171026220223Thu, 26 Oct 2017 22:02 EDTOrthogonal-preserving and surjective cubic stochastic operatorshttps://projecteuclid.org/euclid.afa/1498096869<strong>Farrukh Mukhamedov</strong>, <strong>Ahmad Fadillah Embong</strong>, <strong>Azizi Rosli</strong>. <p><strong>Source: </strong>Annals of Functional Analysis, Volume 8, Number 4, 490--501.</p><p><strong>Abstract:</strong><br/>
In the present paper, we consider cubic stochastic operators, and prove that the surjectivity of such operators is equivalent to their orthogonal-preserving property. In the last section we provide a full description of orthogonal-preserving (respectively, surjective) cubic stochastic operators on the $2$ -dimensional simplex.
</p>projecteuclid.org/euclid.afa/1498096869_20171026220223Thu, 26 Oct 2017 22:02 EDTThe weak Haagerup property for $C^{*}$ -algebrashttps://projecteuclid.org/euclid.afa/1498096870<strong>Qing Meng</strong>. <p><strong>Source: </strong>Annals of Functional Analysis, Volume 8, Number 4, 502--511.</p><p><strong>Abstract:</strong><br/>
We define and study the weak Haagerup property for $C^{*}$ -algebras in this article. A $C^{*}$ -algebra with the Haagerup property always has the weak Haagerup property. We prove that a discrete group has the weak Haagerup property if and only if its reduced group $C^{*}$ -algebra also has that property. Moreover, we consider the permanence of the weak Haagerup property under a few canonical constructions of $C^{*}$ -algebras.
</p>projecteuclid.org/euclid.afa/1498096870_20171026220223Thu, 26 Oct 2017 22:02 EDTA quantitative version of the Johnson–Rosenthal theoremhttps://projecteuclid.org/euclid.afa/1498096868<strong>Dongyang Chen</strong>. <p><strong>Source: </strong>Annals of Functional Analysis, Volume 8, Number 4, 512--519.</p><p><strong>Abstract:</strong><br/> Let $X,Y$ be Banach spaces. We define \begin{equation*}\alpha_{Y}(X)=\sup\{\vert T^{-1}\vert^{-1}:T:Y\rightarrow X\mbox{ is an isomorphism with }\vert T\vert \leq1\}.\end{equation*} If there is no isomorphism from $Y$ to $X$ , we set $\alpha_{Y}(X)=0$ , and \begin{equation*}\gamma_{Y}(X)=\sup\{\delta(T):T:X\rightarrow Y\mbox{ is asurjective operator with }\vert T\vert \leq1\},\end{equation*} where $\delta(T)=\sup\{\delta\gt 0:\delta B_{Y}\subseteq TB_{X}\}$ . If there is no surjective operator from $X$ onto $Y$ , we set $\gamma_{Y}(X)=0$ . We prove that for a separable space $X$ , $\alpha_{l_{1}}(X^{*})=\gamma_{c_{0}}(X)$ and $\alpha_{L_{1}}(X^{*})=\gamma_{C(\Delta)}(X)=\gamma_{C[0,1]}(X)$ . </p>projecteuclid.org/euclid.afa/1498096868_20171026220223Thu, 26 Oct 2017 22:02 EDTSupporting vectors of continuous linear operatorshttps://projecteuclid.org/euclid.afa/1498723219<strong>Clemente Cobos-Sánchez</strong>, <strong>Francisco Javier García-Pacheco</strong>, <strong>Soledad Moreno-Pulido</strong>, <strong>Sol Sáez-Martínez</strong>. <p><strong>Source: </strong>Annals of Functional Analysis, Volume 8, Number 4, 520--530.</p><p><strong>Abstract:</strong><br/>
The set of supporting vectors of a continuous linear operator, that is, the normalized vectors at which the operator attains its norm, is decomposed into its convex components. In the complex case, the set of supporting vectors of a nonzero functional is proved to be path-connected. We also introduce the concept of generalized supporting vectors for a sequence of operators as the normalized vectors that maximize the summation of the squared norm of those operators. We determine the set of generalized supporting vectors for the particular case of a finite sequence of real matrices. Finally, we unveil the relation between the supporting vectors of a real matrix $A$ and the Tikhonov regularization $\min_{x\in\mathbb{R}^{n}}\Vert Ax-b\Vert +\alpha \Vert x\Vert $ reaching the conclusion that, by an appropriate choice of $b$ and $\alpha$ , the supporting vectors of $A$ can be obtained via solving the Tikhonov regularization $\min_{x\in\mathbb{R}^{n}}\Vert Ax-b\Vert +\alpha \Vert x\Vert $ .
</p>projecteuclid.org/euclid.afa/1498723219_20171026220223Thu, 26 Oct 2017 22:02 EDTMinimal reducing subspaces of an operator-weighted shifthttps://projecteuclid.org/euclid.afa/1498723220<strong>Munmun Hazarika</strong>, <strong>Pearl S. Gogoi</strong>. <p><strong>Source: </strong>Annals of Functional Analysis, Volume 8, Number 4, 531--546.</p><p><strong>Abstract:</strong><br/>
We introduce a family $\mathcal{T}$ consisting of invertible matrices with exactly one nonzero entry in each row and each column. The elements of $\mathcal{T}$ are possibly mutually noncommuting, and they need not be normal or self-adjoint. We consider an operator-valued unilateral weighted shift $W$ with a uniformly bounded sequence of weights belonging to $\mathcal{T}$ , and we describe its minimal reducing subspaces.
</p>projecteuclid.org/euclid.afa/1498723220_20171026220223Thu, 26 Oct 2017 22:02 EDTInvolutions in algebras related to second duals of hypergroup algebrashttps://projecteuclid.org/euclid.afa/1504836309<strong>Alireza Medghalchi</strong>, <strong>Ramin Ramezani</strong>. <p><strong>Source: </strong>Annals of Functional Analysis, Volume 8, Number 4, 547--556.</p><p><strong>Abstract:</strong><br/>
Let $K$ be a hypergroup. The purpose of this article is to study the question of involutions on algebras $M(K)^{**}$ , $L(K)^{**}$ , and $L_{c}(K)^{**}$ . We show that the natural involution of $M(K)$ has the canonical extension to $M(K)^{**}$ if and only if the natural involution of $L(K)$ has the canonical extension to $L(K)^{**}$ . Also, we give necessary and sufficient conditions for $M(K)^{**}$ and $L(K)^{**}$ to admit an involution extending the natural involution of $M(K)$ when $K$ is left amenable. Finally, we find the necessary and sufficient conditions for $L_{c}(K)^{**}$ to admit an involution.
</p>projecteuclid.org/euclid.afa/1504836309_20171026220223Thu, 26 Oct 2017 22:02 EDT