Module Amenability and Weak Module Amenability for Second Dual of Banach Algebras
Keywords:
Banach modules, weak amenability, module amenability, weak module amenability, semigroup algebra, inverse semigroupAbstract
In this paper we define the weak module amenability of a Banach algebra which is a Banach module over another Banach algebra
with compatible actions, and show that under some mild conditions weak module amenability of
implies weak module amenability of
. Also among other results, we investigate the relation between module Arens regularity of a Banach algebra and module amenability of its second dual. As a consequence we prove that `
is always weakly module amenable (as an
-module), where
is an inverse semigroup with an upward directed set of idempotents
.
