GENERALIZED NOTION OF WEAK MODULE AMENABILITY

Anahtar Kelimeler:

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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 (a·α)b−a(α·b)for a ∈A and α ∈ A. We then study this concept for an inversesemigroup S, where some examples on(S) and C∗ (S) are given.

Keywords:

Banach modules; Module derivation; Weak amenability; Weak moduleamenability; Inverse semigroup.,

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