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Module Amenability for Semigroup Algebras

2002/05/23 by Massoud Amini, Amini, Massoud
Mathematics · #Advanced Banach Space Theory #Advanced Operator Algebra Research #Advanced Topics in Algebra #math.FA

paper · pdf · doi:10.48550/arxiv.math/0205256

12 pages

arxiv created 2002/05/23 · arxiv updated 2009/11/30

Abstract

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=ℓ1(S) as a Banach module over \mathfrak A=ℓ1(E) is module amenable iff S is amenable. When S is a discrete group, ℓ1(E)=\mathbb C and this is just the celebrated Johnson's theorem.

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