Module Amenability for Semigroup Algebras

الأصل · EN

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