Fair amenability for semigroups

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 $m\in {\ell }^{\infty }(S{)}^{\ast }$ satisfying $m(f)=m(s\ast f)$ whenever $s\ast f\in {\ell }^{\infty }(S)$, thus justifying the nomenclature "fairly amenable''.

26 pages, 10 figures

References in corpus (1)

• $C^{\ast }$-algebras of inverse semigroups: amenability and weak containment

Cited by in corpus (1)

• Amenability and paradoxicality in semigroups and C*-algebras