The concept of amenability for Banach algebras was introduced by Johnson in 1972 [6]. Several modifications of this notion, such as approximate amenability and pseudo-amenability, were introduced in [2] and [4]. In the current paper we investigate the pseudo-amenability of Brandt semigroup algebras. It was shown in [2] and [4] that for the group algebra L(G), amenability, approximate amenabilit...

Liouville property of actions discrete groups can be reformulated in terms existence co-Følner sets. Since every action amenable group is Liouville, the used for proving non-amenability. There are many that defined by strongly transitive actions. In some cases amenability such an open problem. We define <mml:math xmlns:mml="http://www.w3.org/1998/Math...

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 betw...

it was shown in [a. azimifard, e. samei, n. spronk, jfa 256 (2009)] that the zl-amenability constant of a finite group is always at least~$1$, with equality if and only if the group is abelian. it was also shown in [a. azimifard, e. samei, n. spronk, op cit.] that for any finite non-abelian group this invariant is at least $301/300$, but the proof relies crucially on a deep result of d. a. ride...

Let $mathcal{A}$ be a Banach algebra and $X$ be a Banach $mathcal{A}-$bimodule. We study the notion of approximate $n-$ideal amenability for module extension Banach algebras $mathcal{A}oplus X$. First, we describe the structure of ideals of this kind of algebras and we present the necessary and sufficient conditions for a module extension Banach algebra to be approximately n-ideally amenable.

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 dened. 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 short...

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...