Let S be a semigroup. In certain cases we give some characterizations of extreme amenability of S and we show that in these cases extreme left amenability and extreme right amenability of S are equivalent. Also when S is a compact topological semigroup, we characterize extremely left amenable subalgebras of C(S), where C(S) is the space of all continuous bounded real valued functions on S

Abstract We give a short geometric proof of result Soardi and Woess Salvatori that quasitransitive graph is amenable if only its automorphism group unimodular. also strengthen one direction by showing compactly generated totally disconnected locally compact admits proper Lipschitz action on bounded degree then pass via the notion amenability group, which has previously been studied second autho...

In this paper among many other things we prove that the topological left amenability and left amenability of a weighted hypergroup (K, ?) are equivalent. For a normal subgroup H of K, we define a weight function ?? on KIH and obtain connection between left amenability of (K, ?) and (K|H, ??). Let H be a compact subhypergroup of K. We define the weight function on K||H and obtain connection...

Building on previous papers by Anantharaman-Delaroche (AD) we introduce and study the notion of AD-amenability for partial actions Fell bundles over discrete groups. We prove that cross-sectional C*-algebra a bundle is nuclear if only underlying unit fibre AD-amenable. If action globalisable, then it AD-amenable its globalisation Moreover, preserved (weak) equivalence and, using very recent ide...

we survey the recent investigations on (bounded, sequential) approximate connesamenability and pseudo-connes amenability for dual banach algebras. we will discuss thecore problems concerning these notions and address the signi cance of any solutions to themto the development of the eld.

We define a Banach algebra A to be dual if A = (A∗) ∗ for a closed submodule A∗ of A∗. The class of dual Banach algebras includes all W ∗-algebras, but also all algebras M(G) for locally compact groups G, all algebras L(E) for reflexive Banach spaces E, as well as all biduals of Arens regular Banach algebras. The general impression is that amenable, dual Banach algebras are rather the exception...

In this paper, we investigate, for a locally compact groupG, the operator amenability of the Fourier-Stieltjes algebra B(G) and of the reduced Fourier-Stieltjes algebra Br(G). The natural conjecture is that any of these algebras is operator amenable if and only if G is compact. We partially prove this conjecture with mere operator amenability replaced by operator C-amenability for some constant...

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Let G be a locally compact group, and let 1 < p < ∞. In this paper we investigate the injectivity of the left L1(G)-module Lp(G). We define a family of amenability type conditions called (p, q)-amenability, for any 1 ≤ p ≤ q. For a general locally compact group G we show if Lp(G) is injective, then G must be (p, p)-amenable. For a discrete group G we prove that l p(G) is injective if and only i...