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arXiv · 1801.03378

On Connes amenability of upper triangular matrix algebras

S. F. Shariati·A. Pourabbas·A. Sahami
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Abstract

In this paper, we study the notion of Connes amenability for a class of $I\times{I}$-upper triangular matrix algebra $UP(I,\mathcal{A})$, where $\mathcal{A}$ is a dual Banach algebra with a non-zero $wk^\ast$-continuous character and $I$ is a totally ordered set. For this purpose, we characterize the $\phi$-Connes amenability of a dual Banach algebra $\mathcal{A}$ through the existence of a specified net in $\mathcal{A}\hat{\otimes}\mathcal{A}$, where $\phi$ is a non-zero $wk^\ast$-continuous character. Using this, we show that $UP(I,\mathcal{A})$ is Connes amenable if and only if $I$ is singleton and $\mathcal{A}$ is Connes amenable. In addition, some examples of $\phi$-Connes amenable dual Banach algebras, which is not Connes amenable are given.

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BibTeXRIS

S. F. Shariati, A. Pourabbas, A. Sahami. 2018-01-10. On Connes amenability of upper triangular matrix algebras. https://arxiv.org/abs/1801.03378

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