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,  pseudo-amenability and pseudo-Connes amenability of weighted semigroup algebra $ell^1(S,omega)$ are studied. It is proved that pseudo-Connes amenability and pseudo-amenability of weighted group algebra $ell^1(G,omega)$ are the same. Examples are given to show that the class of $sigma$-Connes amenable dual Banach algebras is larger than that of Connes amenable dual Banach algebras.

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...

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...

In this paper, we introduce a weak form of amenability on topological semigroups that call $$\varphi $$ -amenability, where is character semigroup. Some basic properties new notion are obtained and by giving some examples, show definition weaker than the semigroups. As noticeable result, for semigroup S, it shown if S -amenable, then amenable. Moreover, -ergodicity introduced proved under condi...

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

let φ be a w  -continuous homomorphism from a dual banach algebra to c. the notion of φ-connes amenability is studied and some characterizations is given. a type of diagonal for dual banach algebras is de ned. it is proved that the existence of such a diagonal is equivalent to φ-connes amenability. it is also shown that φ-connes amenability is equivalent to so-called φ-splitting of a certain s...

Let $S$ be an inverse semigroup and let $E$ be its subsemigroup of idempotents. In this paper we define the $n$-th module cohomology group of Banach algebras and show that the first module cohomology group $HH^1_{ell^1(E)}(ell^1(S),ell^1(S)^{(n)})$ is zero, for every odd $ninmathbb{N}$. Next, for a Clifford semigroup $S$ we show that $HH^2_{ell^1(E)}(ell^1(S),ell^1(S)^{(n)})$ is a Banach sp...