Amenability of semigroups and common multiples in $\ell^1_+$

Tobias Fritz

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arXiv · 2101.10810

Amenability of semigroups and common multiples in $\ell^1_+$

Tobias Fritz

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Abstract

In this note, we prove that a semigroup $S$ is left amenable if and only if every two nonzero elements of $\ell^1_+(S)$ have a common nonzero right multiple, where $\ell^1_+(S)$ is the positive part of the Banach algebra $\ell^1(S)$, or equivalently the semiring of finite measures on $S$. This characterization of amenability is new even for groups.

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Tobias Fritz. 2021-01-26. Amenability of semigroups and common multiples in $\ell^1_+$. https://arxiv.org/abs/2101.10810

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