Left introverted subspaces of duals of Banach algebras and $WEAK^*-$continuous derivations on dual Banach algebras

Details Left introverted subspaces of duals of Banach algebras and $WEAK^*-$continuous derivations on dual Banach algebras Left introverted subspaces of duals of Banach algebras and $WEAK^*-$continuous derivations on dual Banach algebras

2006-10-05

arxiv.org/abs/math/0610199v2

Mathematics

Functional Analysis

10 pages

Scientific paper

Let $X$ be a left introverted subspace of dual of a Banach algebra. We study $Z_t(X^*),$ the topological center of Banach algebra $X^*$. We fined the topological center of $(X\cA)^*$, when $\cA$ has a bounded right approximate identity and $\cA\subseteq X^*.$ So we introduce a new notation of amenability for a dual Banach algebra $\cal A$. A dual Banach algebra $\cal A$ is weakly Connes-amenable if the first $weak^*-$continuous cohomology group of $\cal A$ with coefficients in $\cal A$ is zero; i.e., $H^1_{w^*}(\cal A, \cal A)=\{o\}$. We study the weak Connes-amenability of some dual Banach algebras.

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