Ideal amenability of Banach algebras on locally compact groups

Details Ideal amenability of Banach algebras on locally compact groups Ideal amenability of Banach algebras on locally compact groups

2005-08-25

arxiv.org/abs/math/0508495v1

Proc. Indian Acad. Sci. (Math. Sci.), Vol. 115, No. 3, August 2005, pp. 319-325

Mathematics

Functional Analysis

7 pages, no figures, no tables

Scientific paper

In this paper we study the ideal amenability of Banach algebras. Let $\cal A$ be a Banach algebra and let $I$ be a closed two-sided ideal in $\cal A$, $\cal A$ is $I$-weakly amenable if $H^{1}({\cal A},I^*)=\{0\}$. Further, $\cal A$ is ideally amenable if $\cal A$ is $I$-weakly amenable for every closed two-sided ideal $I$ in $\cal A$. We know that a continuous homomorphic image of an amenable Banach algebra is again amenable. We show that for ideal amenability the homomorphism property for suitable direct summands is true similar to weak amenability and we apply this result for ideal amenability of Banach algebras on locally compact groups.

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