arXiv 0809.21582008-09-12math.OAmath.FA

Compactness properties of operator multipliers

K. Juschenko, R. H. Levene, I. G. Todorov, L. Turowska

发表信息：: J. Funct. Anal.Volume 256, Issue 11, 2009
DOI：: 10.1016/j.jfa.2008.12.018

英文摘要：

We continue the study of multidimensional operator multipliers initiated in [arXiv:math/0701645]. We introduce the notion of the symbol of an operator multiplier. We characterise completely compact operator multipliers in terms of their symbol as well as in terms of approximation by finite rank multipliers. We give sufficient conditions for the sets of compact and completely compact multipliers to coincide and characterise the cases where an operator multiplier in the minimal tensor product of two C*-algebras is automatically compact. We give a description of multilinear modular completely compact completely bounded maps defined on the direct product of finitely many copies of the C*-algebra of compact operators in terms of tensor products, generalising results of Saar.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

阅读原文

阅读 PDF ↗

arXiv 页面 ↗HTML 原文 ↗

本文内容

英文摘要相关论文

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

继续探索

相关论文

Compactness of Schur-A Multipliers and Haagerup Tensorproduct

In this paper we study the connection between Haagerup tensor product and compactness of Schur $A$-multiplier. In particular, we give a new characterization of elementary $C^{\ast}$-algebra in terms of completely compact Schur $A$-multiplier.

2020-01-21math.OA

非交换 Orlicz 空间上的乘子

Multipliers on Noncommutative Orlicz Spaces

本文研究非交换 Orlicz 空间间乘法算子的存在判据，证明其涵盖已有结果，并比较其与 $L^p$ 空间理论的差异及算子紧性。

2012-05-10math.FAmath.OA

Unbounded multipliers on operator spaces

We introduce unbounded multipliers on operator spaces. These multipliers generalize both, regular operators on Hilbert C*-modules and (bounded) multipliers on operator spaces.

2010-07-22math.FAmath.OA

Multipliers between two operator spaces

In a recent survey paper we introduced one-sided multipliers between two different operator spaces. Here we give some basic theory for these maps.

2003-09-02math.FAmath.OA

Schur multipliers and operator-valued Foguel-Hankel operators

We show that some matrices are Schur multipliers and this is applied to obtain classes of operator-valued Foguel-Hankel operators similar to contractions. This provides partial answers to a problem of K. Davidson and the second author concerning CAR-valued Foguel-Hankel operators.

2005-01-11math.FAmath.OA

Measures of weak non-compactness in spaces of nuclear operators

We show that in the space of nuclear operators from $\ell^q(Λ)$ to $\ell^p(J)$ the two natural ways of measuring weak non-compactness coincide. We also provide explicit formulas for these measures. As a consequence the same is proved for preduals of atomic von Neumann algebras.

2017-11-24math.FAmath.OA

更多相关论文收起更多论文

Schur and operator multipliers

Schur multipliers were introduced by Schur in the early 20th century and have since then found a considerable number of applications in Analysis and enjoyed an intensive development. Apart from the beauty of the subject in itself, sources of interest in them were connections with Perturbation Theory, Harmonic Analysis, the Theory of Operator Integrals and others. Advances in the quantisation of Schur multipliers were recently made by Kissin and Shulman. The aim of the present article is to summarise a part of the ideas and results in the theory of Schur and operator multipliers. We start with …

2009-11-03math.FAmath.OA

Operator algebras with contractive approximate identities: Weak compactness and the spectrum

We continue our study of operator algebras with contractive approximate identities (cais) by presenting a couple of interesting examples of operator algebras with cais, which in particular answer questions raised in previous papers in this series, for example about whether, roughly speaking, `weak compactness' of an operator algebra, or the lack of it, can be seen in the spectra of its elements.

2014-07-05math.FAmath.OA

Multidimensional operator multipliers

We introduce multidimensional Schur multipliers and characterise them generalising well known results by Grothendieck and Peller. We define a multidimensional version of the two dimensional operator multipliers studied recently by Kissin and Shulman. The multidimensional operator multipliers are defined as elements of the minimal tensor product of several C*-algebras satisfying certain boundedness conditions. In the case of commutative C*-algebras, the multidimensional operator multipliers reduce to continuous multidimensional Schur multipliers. We show that the multipliers with respect to som…

2008-03-20math.FAmath.OA

The Calculus of One-Sided $M$-Ideals and Multipliers in Operator Spaces

The theory of one-sided $M$-ideals and multipliers of operator spaces is simultaneously a generalization of classical $M$-ideals, ideals in operator algebras, and aspects of the theory of Hilbert $C^*$-modules and their maps. Here we give a systematic exposition of this theory; a reference tool for `noncommutative functional analysts' who may encounter a one-sided $M$-ideal or multiplier in their work.

2003-09-02math.FAmath.OA

Multipliers for p-Bessel sequences in Banach spaces

Multipliers have been recently introduced as operators for Bessel sequences and frames in Hilbert spaces. These operators are defined by a fixed multiplication pattern (the symbol) which is inserted between the analysis and synthesis operators. In this paper, we will generalize the concept of Bessel multipliers for p-Bessel and p-Riesz sequences in Banach spaces. It will be shown that bounded symbols lead to bounded operators. Symbols converging to zero induce compact operators. Furthermore, we will give sufficient conditions for multipliers to be nuclear operators. Finally, we will show the c…

2010-04-29math.FAmath.OA

The Douglas property for multiplier algebras of operators

For a collection of reproducing kernels k which includes those for the Hardy space of the polydisk and ball and for the Bergman space, k is a complete Pick kernel if and only if the multiplier algebra of the Hilbert space H^2(k) associated to k has the Douglas property. Consequences for solving the operator equation AX=Y are examined.

2011-11-17math.FAmath.OA

Local Operator Multipliers and Positivity

We establish an unbounded version of Stinespring's Theorem and a lifting result for Stinespring representations of completely positive modular maps defined on the space of all compact operators. We apply these results to study positivity for Schur multipliers. We characterise positive local Schur multipliers, and provide a description of positive local Schur multipliers of Toeplitz type. We introduce local operator multipliers as a non-commutative analogue of local Schur multipliers, and obtain a characterisation that extends earlier results concerning operator multipliers and local Schur mult…

2012-06-18math.OA

Module homomorphisms and multipliers on locally compact quantum groups

For a Banach algebra $A$ with a bounded approximate identity, we investigate the $A$-module homomorphisms of certain introverted subspaces of $A^*$, and show that all $A$-module homomorphisms of $A^*$ are normal if and only if $A$ is an ideal of $A^{**}$. We obtain some characterizations of compactness and discreteness for a locally compact quantum group $\G$. Furthermore, in the co-amenable case we prove that the multiplier algebra of $\LL$ can be identified with $\MG.$ As a consequence, we prove that $\G$ is compact if and only if $\LUC={\rm WAP}(\G)$ and $\MG\cong\mathcal{Z}({\rm LUC}(\G)^*…

2009-07-14math.OA

Multipliers and Hereditary Subalgebras of Operator Algebras

We generalize some technical results of Glicksberg to the realm of general operator algebras and use them to give a characterization of open and closed projections in terms of certain multiplier algebras. This generalizes a theorem of J. Wells characterizing an important class of ideals in uniform algebras. The difficult implication in our main theorem is that if a projection is open in an operator algebra, then the multiplier algebra of the associated hereditary subalgebra arises as the closure of the subalgebra with respect to the strict topology of the multiplier algebra of a naturally asso…

2010-10-08math.OA

Operator system structures and extensions of Schur multipliers

For a given C*-algebra $\mathcal{A}$, we establish the existence of maximal and minimal operator $\mathcal{A}$-system structures on an AOU $\mathcal{A}$-space. In the case $\mathcal{A}$ is a W*-algebra, we provide an abstract characterisation of dual operator $\mathcal{A}$-systems, and study the maximal and minimal dual operator $\mathcal{A}$-system structures on a dual AOU $\mathcal{A}$-space. We introduce operator-valued Schur multipliers, and provide a Grothendieck-type characterisation. We study the positive extension problem for a partially defined operator-valued Schur multiplier $φ$ and…

2018-12-16math.OA