Amenability properties of Figà-Talamanca–Herz algebras on inverse semigroups
Volume 233 / 2016
Studia Mathematica 233 (2016), 1-12
MSC: Primary 43A15; Secondary 20M18.
DOI: 10.4064/sm8250-4-2016
Published online: 5 May 2016
Abstract
This paper continues the joint work with A. R. Medghalchi (2012) and the author’s recent work (2015). For an inverse semigroup $S$, it is shown that ${\rm A}_p(S)$ has a bounded approximate identity if and only if $l^1(S)$ is amenable (a generalization of Leptin’s theorem) and that ${\rm A}(S)$, the Fourier algebra of $S$, is operator amenable if and only if $l^1(S)$ is amenable (a generalization of Ruan’s theorem).
