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arXiv · 1310.5589

Fair amenability for semigroups

Josh Deprez
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Abstract

A new flavour of amenability for discrete semigroups is proposed that generalises group amenability and follows from a \Folner-type condition. Some examples are explored, to argue that this new notion better captures some essential ideas of amenability. A semigroup $S$ is left fairly amenable if, and only if, it supports a mean $m\in\ell^\infty(S)^*$ satisfying $m(f) = m(s\ast f)$ whenever $s\ast f\in\ell^\infty(S)$, thus justifying the nomenclature "fairly amenable''.

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Josh Deprez. 2013-10-11. Fair amenability for semigroups. https://doi.org/10.1016/j.jalgebra.2016.03.049

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