Module Amenability for Semigroup Algebras

Details Module Amenability for Semigroup Algebras Module Amenability for Semigroup Algebras

2002-05-23

arxiv.org/abs/math/0205256v1

Mathematics

Functional Analysis

12 pages

Scientific paper

We extend the concept of amenability of a Banach algebra $A$ to the case that there is an extra $\mathfrak A$-module structure on $A$, and show that when $S$ is an inverse semigroup with subsemigroup $E$ of idempotents, then $A=\ell^1(S)$ as a Banach module over $\mathfrak A=\ell^1(E)$ is module amenable iff $S$ is amenable. When $S$ is a discrete group, $\ell^1(E)=\mathbb C$ and this is just the celebrated Johnson's theorem.

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