Module amenability for Banach modules

D. Ebrahimi Bagha; M. Amini

doi:10.4067/S0719-06462011000200007

Authors

D. Ebrahimi Bagha Department of Mathematics, Islamic Azad University, Central Tehran Branch, Tehran, Iran.
M. Amini Department of Mathematics, Tarbiat Modares University, P.O.Box 14115-175, Tehran, Iran.

DOI:

https://doi.org/10.4067/S0719-06462011000200007

Keywords:

Banach modules, module amenability, weak module amenability, semigroup algebra, inverse semigroup

Abstract

We study the module amenability of Banach modules. This is a natural generalization of Johnson‘s amenability of Banach algebras. As an example we show that for a discrete abelian group G, â„“^p(G) is amenable as an â„“¹(G)-module if and only if G is amenable, where â„“¹ (G) is a Banach algebra with pointwise multiplication.