## 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.

### MSC:

 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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