Derivations into n-th duals of ideals of Banach algebras

Details Derivations into n-th duals of ideals of Banach algebras Derivations into n-th duals of ideals of Banach algebras

2006-10-05

arxiv.org/abs/math/0610171v1

Mathematics

Functional Analysis

11 page

Scientific paper

We introduce two notions of amenability for a Banach algebra $\cal A$. Let $n\in \Bbb N$ and let $I$ be a closed two-sided ideal in $\cal A$, $\cal A$ is $n-I-$weakly amenable if the first cohomology group of $\cal A$ with coefficients in the n-th dual space $I^{(n)}$ is zero; i.e., $H^1({\cal A},I^{(n)})=\{0\}$. Further, $\cal A$ is n-ideally amenable if $\cal A$ is $n-I-$weakly amenable for every closed two-sided ideal $I$ in $\cal A$. We find some relationships of $n-I-$ weak amenability and $m-J-$ weak amenability for some different m and n or for different closed ideals $I$ and $J$ of $\cal A$.

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