Module amenability of the second dual and module topological center of semigroup algebras. (English) Zbl 1200.43001

The authors continue their work on module amenability and module Arens regularity (see M. Amini [Semigroup Forum 69, 243–254 (2004; Zbl 1059.43001); Corrigendum ibid. 72, 493 (2006)] and R. Rezavand, M. Amini, M. H. Sattari and D. E. Bagha [Semigroup Forum 77, 300–305 (2008; Zbl 1161.46026); Corrigendum ibid. 79, 214–215 (2009)]). They now define the module topological center, consider the module amenability of second duals, and study the second dual of \(\ell^1(S)\) when \(S\) is an inverse semigroup with an upwardly directed set of idempotents.


43A07 Means on groups, semigroups, etc.; amenable groups
46H25 Normed modules and Banach modules, topological modules (if not placed in 13-XX or 16-XX)
20M25 Semigroup rings, multiplicative semigroups of rings
20M18 Inverse semigroups
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