Module amenability for semigroup algebras. (English) Zbl 1059.43001

Semigroup Forum 69, No. 2, 243-254 (2004); corrigendum ibid. 72, No. 3, 493 (2006).
Summary: We extend the concept of amenability of a Banach algebra \(A\) to the case where there is an extra \({\mathfrak A}\)-module structure on \(A\) and show that when \(S\) is an inverse semigroup with subsemigroup \(E\) of idempotents, then \(A=\ell^1(S)\) as a Banach module over \({\mathfrak A}=\ell^1(E)\) is module amenable if and only if \(S\) is amenable. When \(S\) is a discrete group, \(\ell^1(E)=\mathbb{C}\) and this is just Johnson’s theorem.
Editorial remark: For the corrigendum see doi:10.1007/s00233-005-0556-3.


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)
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