, Volume 86, Issue 2, pp 279-288
Date: 11 Sep 2012

Super module amenability of inverse semigroup algebras

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Abstract

In this paper we compare the notions of super amenability and super module amenability of Banach algebras, which are Banach modules over another Banach algebra with compatible actions. We find conditions for the two notions to be equivalent. In particular, we study arbitrary module actions of l 1(E S ) on l 1(S) for an inverse semigroup S with the set of idempotents E S and show that under certain conditions, l 1(S) is super module amenable if and only if S is finite. We also study the super module amenability of l 1(S)∗∗ and module biprojectivity of l 1(S), for arbitrary actions.

Communicated by Jerome A. Goldstein.
The third author was partly supported by a grant from IPM (No. 90430215).