Module approximate amenability for semigroup algebras

In this study, we introduce module approximate amenability. Indeed, we extend the concept of approximate amenability of Banach algebra A to the case that there is an extra U-module structure on A and we show that l1(S) is module approximately amenable if and only if S is amenable, where, S is an inverse semigroup with subsemigroup E of idempotents and l1(S)has l1(E)-module structure. © 2009 Asian Network for Scientific Information.