$varphi$-Connes amenability of dual Banach algebras

Authors

  • A. Ghaffari Department of‎ ‎Mathematics‎, ‎Semnan University‎, ‎P.O‎. ‎Box 35195-363‎, ‎Semnan‎, ‎Iran.
  • S. Javadi Department of‎ ‎Mathematics, ‎Semnan University, ‎P.O‎. ‎Box 35195-363‎, ‎Semnan‎, ‎Iran.
Abstract:

‎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.

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Journal title

volume 43  issue 1

pages  25- 39

publication date 2017-02-22

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