Amenable actions of inverse semigroups

Abstract

We say that an action of a countable discrete inverse semigroup on a locally compact Hausdorff space is amenable if its groupoid of germs is amenable in the sense of Anantharaman-Delaroche and Renault. We then show that for a given inverse semigroup \(S\), the action of \(S\) on its spectrum is amenable if and only if every action of \(S\) is amenable.