$\varphi$-Connes amenability of dual Banach algebras

Document Type : Research Paper


1 Department of‎ ‎Mathematics‎, ‎Semnan University‎, ‎P.O‎. ‎Box 35195-363‎, ‎Semnan‎, ‎Iran.

2 Department of‎ ‎Mathematics, ‎Semnan University, ‎P.O‎. ‎Box 35195-363‎, ‎Semnan‎, ‎Iran.


‎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 $\mathcal{A}_*$‎. ‎Several characterizations of‎ ‎$\varphi$-Connes amenability are given‎. ‎We also prove that the‎ ‎following are equivalent for a unital weakly cancellative‎ ‎semigroup algebra $l^1(S)$‎:
(i) $S$ is $\chi$-amenable‎.
(ii) $l^1(S)$ is $\hat{\chi}$-Connes amenable‎.
(iii) $l^1(S)$ has a $\hat{\chi}$-normal‎, ‎virtual diagonal‎.


Main Subjects

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