Module super-amenability for semigroup algebras

Details Module super-amenability for semigroup algebras Module super-amenability for semigroup algebras

2009-12-23

arxiv.org/abs/0912.4624v1

Mathematics

Functional Analysis

9 pages

Scientific paper

Let $S$ be an inverse semigroup with the set of idempotents $E$. In this paper we define the module super-amenability of a Banach algebra which is a Banach module over another Banach algebra with compatible actions, and show that when $E$ is upward directed and acts on $S$ trivially from left and by multiplication from right, the semigroup algebra $ \ell ^{1}(S)$ is $\ell^{1}(E)$-module super-amenable if and only if an appropriate group homomorphic image of $S$ is finite.

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