Amenability for discrete convolution semigroup algebras. (English) Zbl 0748.46027

Summary: For any semigroup \(S\) we show that if the convolution algebra \(\ell^ 1(S,\omega)\) is amenable for some weight \(\omega\) then \(S\) is a regular semigroup with a finite number of idempotents: in particular, for the case of an inverse semigroup \(S\), we have \(\ell^ 1(S)\) amenable if and only if \(S\) has a finite number of idempotents and every subgroup of \(S\) is amenable. Various known results on amenability are shown to be easy corollaries of our results.


46H15 Representations of topological algebras
46B45 Banach sequence spaces
46H25 Normed modules and Banach modules, topological modules (if not placed in 13-XX or 16-XX)
46M05 Tensor products in functional analysis
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