Module Amenability of Banach Algebras

Abstract

Let and be Banach algebras, and let  be a Banach -bimodule. In this paper, at first we generalize some theorems from amenable Banach algebras into module amenable Banach algebras. We show that when  and  are commutative Banach -bimodules, and  is module amenable, where  is two-sided closed ideal in , then  is module amenable. By this, we show that if  is a two sided ideal in an amenable inverse semigroup , then  is amenable.