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arXiv · 2104.03230

An analytic criterion for the local finiteness of a countable semigroup

Oleg Aristov
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Abstract

We prove that a countable semigroup $S$ is locally finite if and only if the Arens-Michael envelope of its semigroup algebra is a $(DF)$-space. This is a counterpart to a recent result of the author, which asserts that $S$ is finitely generated if and only if the Arens-Michael envelope is a Fr\'echet space.

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Oleg Aristov. 2021-04-07. An analytic criterion for the local finiteness of a countable semigroup. https://arxiv.org/abs/2104.03230

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