Module amenability of the second dual and module topological center of semigroup algebras

2009/12/20 by Massoud Amini, Amini, Massoud, Abasalt Bodaghi +3
Mathematics · #Advanced Banach Space Theory #Advanced Operator Algebra Research #Advanced Topics in Algebra #math.FA #msc:46H25

paper · pdf · doi:10.48550/arxiv.0912.4003

9 pages

arxiv created 2010/01/04 · arxiv updated 2010/01/14

Abstract

Let S be an inverse semigroup with an upward directed set of idempotents E. In this paper we define the module topological center of second dual of a Banach algebra which is a Banach module over another Banach algebra with compatible actions, and find it for ℓ ¹(S)^** (as an ℓ¹(E)-module). We also prove that ℓ ¹(S)^** is ℓ¹(E)-module amenable if and only if an appropriate group homomorphic image of S is finite.

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