Abstract
We prove that a countable semigroup \( S \) is locally finite if and only if the Arens–Michael envelope of the semigroup algebra of \( S \) is a \( (DF) \)-space. This is a counterpart to the author’s recent result asserting that \( S \) is finitely generated if and only if the Arens–Michael envelope is a Fréchet space.
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The author thanks the referee for the useful comments that improved the presentation.
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Translated from Sibirskii Matematicheskii Zhurnal, 2022, Vol. 63, No. 3, pp. 510–515. https://doi.org/10.33048/smzh.2022.63.303
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Aristov, O.Y. An Analytical Criterion for the Local Finiteness of a Countable Semigroup. Sib Math J 63, 421–424 (2022). https://doi.org/10.1134/S003744662203003X
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DOI: https://doi.org/10.1134/S003744662203003X