Related papers: Amenable representations and dynamics of the unit …

Let $G$ be a locally compact group and $(\Phi, \Psi)$ be a complementary pair of $N$-functions. In this paper, using the powerful tool of porosity, it is proved that when $G$ is an amenable group, then the Fig\`a-Talamanca-Herz-Orlicz…

The aim of this paper is to extend the framework of the spectral method for proving property (T) to the class of reflexive Banach spaces and present a condition implying that every affine isometric action of a given group $G$ on a reflexive…

The goal of this article is to study results and examples concerning finitely presented covers of finitely generated amenable groups. We collect examples of groups $G$ with the following properties: (i) $G$ is finitely generated, (ii) $G$…

We study universal properties of locally compact G-spaces for countable infinite groups G. In particular we consider open invariant subsets of the \beta-compactification of G (which is a G-space in a natural way), and their minimal closed…

In this note we collect several characterizations of unitary representations $(\pi, \mathcal{H})$ of a finite dimensional Lie group $G$ which are trace class, i.e., for each compactly supported smooth function $f$ on $G$, the operator…

We prove several theorems relating amenability of groups in various categories (discrete, definable, topological, automorphism group) to model-theoretic invariants (quotients by connected components, Lascar Galois group, G-compactness,…

Let $G$ be $S_{\mathbb{N}}$, the finitary permutation (i.e. permutations with finite support) group on positive integers $\mathbb{N}$. We prove that $G$ has the invariant von Neumann subalgebras rigidity (ISR, for short) property as…

Let $R$ be an algebraically closed field and $\ell$ be its characteristic. Let $G$ be a locally profinite group having a compact open subgroup of invertible pro-order in $R$. Take $N$ a closed subgroup of $G$ exhausted by compact subgroups…

We examine Hilbert-Schmidt stability (HS-stability) of discrete amenable groups from several angles. We give a short, elementary proof that finitely generated nilpotent groups are HS-stable. We investigate the permanence of HS-stability…

For any countable group, and also for any locally compact second countable, compactly generated topological group, G, we show the existence of a "universal" hypercyclic (i.e. topologically transitive) representation on a Hilbert space, in…

Let $H$ be an infinite-dimensional separable Hilbert space and let $(X,d,\mu)$ be a metric measure space satisfying the doubling and upper Alhfors regularity conditions at small scale. We prove that every bounded continuous tight frame…

Johnson's characterization of amenable groups states that a discrete group $\Gamma$ is amenable if and only if $H_b^{n \geq 1}(\Gamma; V) = 0$ for all dual normed $\mathbb{R}[\Gamma]$-modules V. In this paper, we extend the previous result…

We generalize the notion of isoperimetric profiles of finitely generated groups to their actions by measuring the boundary of finite subgraphings of the orbit graphing. We prove that like the classical isoperimetric profiles for groups,…

We show that amenability of a group acting by homeomorphisms can be deduced from a certain local property of the action and recurrency of the orbital Schreier graphs. This covers amenability of a wide class groups, the amenability of which…

We introduce the notion of first order amenability, as a property of a first order theory $T$: every complete type over $\emptyset$, in possibly infinitely many variables, extends to an automorphism-invariant global Keisler measure in the…

Let $G$ be a finitely generated amenable group. We study the space of shifts on $G$ over a given finite alphabet $A$. We show that the zero entropy shifts are generic in this space, and that more generally the shifts of entropy $c$ are…

Let K be a fine hyperbolic graph and G be a group acting on K with finite quotient. We prove that G is exact provided that all vertex stabilizers are exact. In particular, a relatively hyperbolic group is exact if all its peripheral groups…

We show that for any abelian topological group $G$ and arbitrary diffused submeasure $\mu$, every continuous action of $L_0(\mu,G)$ on a compact space has a fixed point. This generalizes earlier results of Herer and Christensen, Glasner,…

For locally compact groups, we define an analogue to Yu's property A that he defined for discrete metric spaces. We show that our property A for locally compact groups agrees with Roe's notion of property A for proper metric spaces, defined…

In this work we introduce and study a new notion of amenability for actions of locally compact groups on $C^*$-algebras. Our definition extends the definition of amenability for actions of discrete groups due to Claire…