The Structure of φ-Module Amenable Banach Algebras

Abstract EN

We study the concept of φ-module amenability of Banach algebras, which are Banach modules over another Banach algebra with compatible actions.

Also, we compare the notions of φ-amenability and φ-module amenability of Banach algebras.

As a consequence, we show that, if S is an inverse semigroup with finite set E of idempotents and l1S is a commutative Banach l1E-module, then l1S** is φ**-module amenable if and only if S is finite, when φ∈Homl1El1S is an epimorphism.

Indeed, we have generalized a well-known result due to Ghahramani et al.

(1996).