Character Connes-amenability of dual Banach algebras

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• 作者：Behrouz Shojaee ; Massoud Amini
• 关键词：Dual Banach algebras ; Connes amenability ; Character Connes amenability
• 刊名：Periodica Mathematica Hungarica
• 出版年：2017
• 出版时间：March 2017
• 年：2017
• 卷：74
• 期：1
• 页码：31-39
• 全文大小：
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics, general;
• 出版者：Springer Netherlands
• ISSN：1588-2829
• 卷排序：74

文摘

The concept of left character Connes-amenability for a dual Banach algebra \({\mathcal {A}}\) is introduced. We obtain a cohomological characterization of left character Connes-amenability as well as the relation between left \(\varphi \)-Connes-amenability and existence of left \(\varphi \)-normal virtual diagonals for a \(\omega ^{*}\)-continuous character \(\varphi \). We prove that left character amenability of \({\mathcal {A}}\) is equivalent to left character Connes-amenability of \({\mathcal {A}}^{**}\) when \({\mathcal {A}}\) is Arens regular. Moreover for a locally compact group G, we show that M(G) is left character Connes-amenable. In addition by means of some examples we show that for the new notion, the corresponding class of dual Banach algebras is larger than Connes-amenable dual Banach algebras.