On connes amenability of upper triangular matrix algebras

被引：0
|
作者：
Shariati, S.F. [1 ]
Pourabbas, A. [1 ]
Sahami, A. [2 ]
机构：
[1] Faculty of Mathematics and Computer Science, Amirkabir University of Technology, 424 Hafez Avenue, Tehran,15914, Iran
[2] Department of Mathematics, Faculty of Basic Sciences, Ilam University, P.O. Box 69315-516, Ilam, Iran
来源：
UPB Scientific Bulletin, Series A: Applied Mathematics and Physics | 2018年 / 80卷 / 02期
关键词：
Set theory - Banach spaces;
D O I：
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学科分类号：
摘要：
In this paper, we study the notion of Connes amenability for a class of I × I-upper triangular matrix algebra UP(I,A), where A is a dual Banach algebra with a non-zero wk∗-continuous character and I is a totally ordered set. For this purpose, we characterize the φ-Connes amenability of a dual Banach algebra A through the existence of a specified net in A⊗A, where φ is a non-zero wk∗-continuous character. Using this, we show that UP(I,A) is Connes amenable if and only if I is singleton and A is Connes amenable. In addition, some examples of φ-Connes amenable dual Banach algebras, which is not Connes amenable are given. © 2018 Politechnica University of Bucharest. All rights reserved.
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页码：145 / 152
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