Derivation into duals of ideals of Banach algebras

Details Derivation into duals of ideals of Banach algebras Derivation into duals of ideals of Banach algebras

2005-03-05

arxiv.org/abs/math/0503093v1

Proc. Indian Acad. Sci. (Math. Sci.), Vol. 114, No. 4, November 2004, pp. 399-408

Mathematics

Functional Analysis

10 pages

Scientific paper

We introduce two notions of amenability for a Banach algebra $\cal A$. Let $I$ be a closed two-sided ideal in $\cal A$, we say $\cal A$ is $I$-weakly amenable if the first cohomology group of $\cal A$ with coefficients in the dual space $I^*$ is zero; i.e., $H^1({\cal A},I^*)=\{0\}$, and, $\cal A$ is ideally amenable if $\cal A$ is $I$-weakly amenable for every closed two-sided ideal $I$ in $\cal A$. We relate these concepts to weak amenability of Banach algebras. We also show that ideal amenability is different from amenability and weak amenability. We study the $I$-weak amenability of a Banach algebra $\cal A$ for some special closed two-sided\break ideal $I$.

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