$varphi$-connes amenability of dual banach algebras
چکیده
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.