We argue that weak containment is an appropriate notion of amenability for inverse semigroups. Given an inverse semigroup S and a homomorphism φ of S onto a group G, we show, under an assumption on ker(φ), that S has weak containment if and only if G is amenable and ker(φ) has weak containment. Using Fell bundle amenability, we find a related result for inverse semigroups with zero. We show tha...

We study skew-amenable topological groups, i.e., those admitting a left-invariant mean on the space of bounded real-valued functions left-uniformly continuous in sense Bourbaki. prove characterizations skew-amenability for groups isometries and automorphisms, clarify connection with extensive amenability group actions, establish Følner-type characterization, discuss closure properties class gro...

Using the recently developed notion of a Herz-Schur multiplier C*-dynamical system we introduce weak amenability C*- and W*-dynamical systems. As special case recover Haagerup's characterisation discrete group. We also consider generalisation Fourier algebra its multipliers to crossed products.

We prove that $Out(F_N)$ is boundary amenable. This also holds more generally for $Out(G)$, where $G$ either a toral relatively hyperbolic group or right-angled Artin group. As consequence, all these groups satisfy the Novikov conjecture on higher signatures.

In this paper, we introduce actions of fusion algebras on unital $$C^*$$ -algebras, and define amenability for algebraic actions. Motivated by S. Neshveyev et al.’s work, considering the representation ring a compact quantum group as algebra, canonical (for short, CFA) form discrete action space. Furthermore, through CFA form, FA-amenability actions, present some basic connections between FA-am...

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 ...

In this paper we introduce the notion of $varphi$-commutativity for a Banach algebra $A$, where $varphi$ is a continuous homomorphism on $A$ and study the concept of $varphi$-weak amenability for $varphi$-commutative Banach algebras. We give an example to show that the class of $varphi$-weakly amenable Banach algebras is larger than that of weakly amenable commutative Banach algebras. We charac...