GENERALIZED NOTION OF WEAK MODULE AMENABILITY

In the present paper, we introduce a new notion of weak module amenability for Banach algebras which is related to module homomorphisms. Among other results, we investigate the relationship between this concept for a Banach algebra A which is a Banach A-bimodule with compatible actions, and the quotient Banach algebra A/J where J is the closed ideal of A generated by elements of the form (a.α)b-a(α.b) for a in A and α in A. We then study this concept for an inverse semigroup S, where some examples on ℓ¹(S) and C*(S) are given.