We study the concept of α-amenability of commutative hypergroups K. We establish several characterizations of α-amenability by combining results of [1] and [2] and adding the Glicksberg-Reiter property. In addition, as examples compact K and discrete polynomial hypergroups on N0 are discussed. 2000 Mathematics Subject Classification: Primary 43A62, Secondary 46H25

Abstract. For any finite unital commutative idempotent semigroup S, a unital semilattice, we show how to compute the amenability constant of its semigroup algebra l(S), which is always of the form 4n+1. We then show that these give lower bounds to amenability constants of certain Banach algebras graded over semilattices. Our theory applies to certain natural subalgebras of Fourier-Stieltjes alg...

We first show that co-amenability does not pass to subgroups, answering a question asked by Eymard in 1972. We then address address coamenability for von Neumann algebras, describing notably how it relates to the former. Co-amenable subgroups A subgroup H of a group G is called co-amenable in G if it has the following relative fixed point property: Every continuous affine G-action on a convex c...

We discuss some techniques related to equivariant compactifications of uniform spaces and amenability of topological groups. In particular, we give a new proof of a recent result by Glasner and Weiss describing the universal minimal flow of the infinite symmetric group S∞ with the standard Polish topology, and extend Bekka’s concept of an amenable representation, enabling one to deduce non-amen...

In 2005, A. Abdollahi and A. Rejali, studied the relations betweenparadoxical decomposition and configuration for semigroups. In thepresent paper, we introduce one other concept of amenability typeon semigroups and groups which includes amenability of semigroupsand inner-amenability of groups. We have extend the previous knownresults to semigroups and groups satisfying this concept.

We study actions of discrete groups on Hilbert C-modules induced from topological actions on compact Hausdorff spaces. We prove that amenable actions give rise to proper affine isometric actions, provided there is a quasiinvariant measure which is sufficiently close to being invariant in a certain sense. This provides conditions on non-amenability of actions. The notion of amenability of group ...