Johnson pseudo-Connes amenability of dual Banach algebras

Abstract

We introduce the notion of Johnson pseudo-Connes amenability for dual Banach algebras. We sudy the relation between this new notion to various notions of Connes amenability. We prove that for a locally compact group \(G\), \(M(G)\) is Johnson pseudo-Connes amenable if and only if \(G\) is amenable. Also we show that for every non-empty set \(I\), \(M_I(\mathbb{C})\) under this new notion is forced to have a finite index. Finally, we provide some examples of certain dual Banach algebras and we study its Johnson pseudo-Connes amenability.