arXiv 2104.032302021-04math.FA

An analytic criterion for the local finiteness of a countable semigroup

Oleg Aristov

备注：: versio 4, 5 pages
发表信息：: Siberian Math. J., 63:3 (2022), 421-424

英文摘要：

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 Fréchet space.

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