Multidimensional operator multipliers
Multidimensional operator multipliers
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DOI：
10.1090/s0002-9947-09-04771-0
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发表时间：
2007-01
影响因子：
1.3
通讯作者：
K. Juschenko;I. Todorov;L. Turowska
中科院分区：
文献类型：
--
作者：
K. Juschenko;I. Todorov;L. Turowska
我们引入多维 Schur 乘子并对其进行表征，概括了 Grothendieck 和 Peller 的众所周知的结果。我们定义了 Kissin 和 Shulman 最近研究的二维算子乘数的多维版本。多维算子乘子被定义为满足某些有界条件的几个C*代数的最小张量积的元素。在交换 C * 代数的情况下，多维算子乘子简化为连续多维 Schur 乘子。我们证明，如果将表示替换为近似等效的表示，则相对于相应 C * 代数的某些给定表示的乘数不会改变。我们建立了 Grothendieck 和 Peller 表征的非交换和多维版本，它表明通用算子乘子可以作为相应 C * 代数的代数张量积的元素的某些弱极限来获得。
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 some given representations of the corresponding C * -algebras do not change if the representations are replaced by approximately equivalent ones. We establish a non-commutative and multidimensional version of the characterisations by Grothendieck and Peller which shows that universal operator multipliers can be obtained as certain weak limits of elements of the algebraic tensor product of the corresponding C * -algebras.