Fair amenability for semigroups. (English) Zbl 1338.43001
Summary: A new flavour of amenability for discrete semigroups is proposed that generalises group amenability and follows from a Følner-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 \(m \in \ell^\infty(S)^\ast\) satisfying \(m(f) = m(s \ast f)\) whenever \(s \ast f \in \ell^\infty(S)\), thus justifying the nomenclature “fairly amenable”.
MSC:
| 43A07 | Means on groups, semigroups, etc.; amenable groups |
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