Abstract
We extend the concept of amenability of a Banach algebra A to the case that there is an extra \A-module structure on A, and show that when S is an inverse semigroup with subsemigroup E of idempotents, then A = \ell1(S) as a Banach module over \A = \ell1(E) is module amenable if and only if S is amenable. When S is a discrete group, \ell1(E) = ℂ and this is just the Johnson’s theorem.
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