Related papers: On Amenable and Coamenable Coideals

We prove several results on the permanence of weak amenability and the Haagerup property for discrete quantum groups. In particular, we improve known facts on free products by allowing amalgamation over a finite quantum subgroup. We also…

This text surveys classical and recent results in the field of amenability of groups, from a combinatorial standpoint. It has served as the support of courses at the University of G\"ottingen and the \'Ecole Normale Sup\'erieure. The goals…

In recent work of the authors the notion of a derivation being approximately semi-inner arose as a tool for investigating (approximate) amenability questions for Banach algebras. Here we investigate this property in its own right, together…

Let G be a locally compact group, and let 1 < p < \infty. In this paper we investigate the injectivity of the left L^1(G)-module L^p(G). We define a family of amenability type conditions called (p,q)-amenability, for any 1 <= p <= q. For a…

In this paper, we show that there is a net for amenable transformation groups like F{\o}lner net for amenable groups and investigate amenability of a transformation group constructed by semidirect product of groups. We introduce inner…

Given a locally compact quantum group $\mathbb G$, we define and study representations and C$^\ast$-completions of the convolution algebra $L_1(\mathbb G)$ associated with various linear subspaces of the multiplier algebra $C_b(\mathbb G)$.…

In this paper, we countinue our work in \cite{11}. We show that $L^{1}(G,w)$ is $\phi_{0}$-biprojective if and only if $G$ is compact, where $\phi_{0}$ is the augmentation character. We introduce the notions of character Johnson amenability…

We show that for a Banach algebra $A$ with a bounded approximate identity, the amenability of the projective tensor product of A with A, the amenability of the projective tensor product of A with A^{op}and the amenability of A are…

We consider the Fourier-Stietljes algebra B(G) of a locally compact group G. We show that operator amenablility of B(G) implies that a certain semitolpological compactification of G admits only finitely many idempotents. In the case that G…

We show that an amenable Invariant Random Subgroup of a locally compact second countable group lives in the amenable radical. This answers a question raised in the introduction of the paper "Kesten's Theorem for Invariant Random Subgroup"…

We investigate the notions of amenability and its related homological notions for a class of $I\times I$-upper triangular matrix algebra, say $UP(I,A)$, where $A$ is a Banach algebra equipped with a non-zero character. We show that…

We show that an \'etale groupoid which is strongly amenable at infinity is amenable whenever its full and reduced $C^*$-algebras coincide.

Every topological group $G$ has some natural compactifications which can be a useful tool of studying $G$. We discuss the following constructions: (1) the greatest ambit $S(G)$ is the compactification corresponding to the algebra of all…

Building on previous papers by Anantharaman-Delaroche (AD) we introduce and study the notion of AD-amenability for partial actions and Fell bundles over discrete groups. We prove that the cross-sectional C*-algebra of a Fell bundle is…

Let $G$ be a countable group. We introduce several equivalence relations on the set ${\rm Sub}(G)$ of subgroups of $G$, defined by properties of the quasi-regular representations $\lambda_{G/H}$ associated to $H\in {\rm Sub}(G)$ and compare…

Commability is the finest equivalence relation between locally compact groups such that $G$ and $H$ are equivalent whenever there is a continuous proper homomorphism $G \to H$ with cocompact image. Answering a question of Cornulier, we show…

Inner amenability is a bridge between amenability of an object and amenability of its operator algebras. It is an open problem of Ananantharman-Delaroche to decide whether all \'etale groupoids are inner amenable. Approximate lattices and…

Let $\mathbb{G}$ be a locally compact quantum group, and $A,B$ von Neumann algebras on which $\mathbb{G}$ acts. We refer to these as $\mathbb{G}$-dynamical W$^*$-algebras. We make a study of $\mathbb{G}$-equivariant $A$-$B$-correspondences,…

We show that if $\Gamma\curvearrowright (X^\Gamma,\mu^\Gamma)$ is a Bernoulli action of an i.c.c. nonamenable group $\Gamma$ which is weakly amenable with Cowling-Haagerup constant $1$, and $\Lambda\curvearrowright(Y,\nu)$ is a free ergodic…

The main goal of this note is to suggest an algebraic approach to the quasi-isometric classification of partially commutative groups (alias right-angled Artin groups). More precisely, we conjecture that if the partially commutative groups…