Module amenability for Banach modules

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.