GENERALIZED NOTION OF WEAK MODULE AMENABILITY

In the present paper, we introduce a new notion of weak moduleamenability for Banach algebras which is related to module homomorphisms. Among other results, we investigate the relationship betweenthis concept for a Banach algebraA which is a Banach A-bimodule withcompatible actions, and the quotient Banach algebraA/J where J isthe closed ideal ofA generated by elements of the form insert ignore into journalissuearticles values(a·α);b−ainsert ignore into journalissuearticles values(α·b);for a ∈A and α ∈ A. We then study this concept for an inversesemigroup S, where some examples oninsert ignore into journalissuearticles values(S); and C∗ insert ignore into journalissuearticles values(S); are given.