The Structure of φ-Module Amenable Banach Algebras - Mahmood Lashkarizadeh Bami; Mohammad Valaei; Massoud Amini (Abstract and Applied Analysis)
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).