Module character amenability of Banach algebras

摘要

In this paper we introduce the notion of module character amenable Banach algebras and show that they possess module character virtual (approximate) diagonals. As a basic example, we show that for an inverse semigroup S with the set of idempotents E, the semigroup algebra ? ~1(S) is module character amenable as an ? ~1(E)-module if only if S is amenable.