$varphi$-connes amenability of dual banach algebras

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• $\varphi$-Connes amenability of dual Banach algebras

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  Generalizing the notion of character amenability for Banach algebras, we study the concept of $\varphi$-Connes amenability of a dual Banach algebra $\mathcal{A}$ with predual $\mathcal{A}_*$, where $\varphi$ is a homomorphism from $\mathcal{A}$ onto $\Bbb C$ that lies in $\mathca

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  In this paper we define $\varphi$-Connes module amenability ofa dual Banach algebra $\mathcal{A}$ where $\varphi$ is a bounded $w_{k^*}$-modulehomomorphism from $\mathcal{A}$ to $\mathcal{A}$. We are mainlyconcerned with the study of $\varphi$-module normalvirtual diagonals. We s