Related papers: On amenability and groups of measurable maps

We show that any second-countable \'etale groupoid with polynomial growth is topologically amenable. If its unit space is compact and metrizable, we show that the groupoid has weak $m$-comparison. Thus if the groupoid is also ample and…

Given any amenable group $G$ (with a left Haar measure $|\cdot|$ or $dg$), we can select out a \textit{F{\o}lner subnet} $\{F_\theta,\theta\in\Theta\}$ from any left F{\o}lner net in $G$, which is \textit{$L^\infty$-admissible}, namely, for…

For two not necessarily commutative topological groups G and T, let H(G,T) denote the space of all continuous homomorphisms from G to T with the compact-open topology. We prove that if G is metrizable and T is compact then H(G,T) is a…

Let $K$ be a locally compact field of characteristic 0. Let $G$ be a linear algebraic group defined over $K$, acting algebraically on an algebraic variety $V$. We prove that the action of $G(K)$ (the group of $K$-rational points of $G$) on…

We define and study notions of amenability and skew-amenability of continuous actions of topological groups on compact topological spaces. Our main motivation is the question under what conditions amenability of a topological group passes…

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…

Building on our previous work, we study the non-relative homology of quantum group convolution algebras. Our main result establishes the equivalence of amenability of a locally compact quantum group $\mathbb{G}$ and 1-injectivity of…

A topological gyrogroup is a gyrogroup endowed with a topology such that the binary operation is jointly continuous and the inverse mapping is also continuous. It is shown that each compact subset of a topological gyrogroup with an…

We provide a general criterion to deduce maximal amenability of von Neumann subalgebras $L\Lambda \subset L\Gamma$ arising from amenable subgroups $\Lambda$ of discrete countable groups $\Gamma$. The criterion is expressed in terms of…

We study amenability of definable and topological groups. Among our main technical tools is an elaboration on and strengthening of the Massicot-Wagner version of the stabilizer theorem, and some results around measures. As an application we…

In this article, we introduce and explore the notion of topological amenability in the broad setting of (locally compact) semihypergroups. We acquire several stationary, ergodic and Banach algebraic characterizations of the same in terms of…

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…

In this note we state a conjecture that characterizes unital C*-algebras for which the unitary group is amenable as a topological group in the norm topology. We prove the conjecture for simple, separable, stably finite, unital, $\mathcal…

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

In this note we prove that if a finitely generated amenable group admits a regular map to a direct product of a hyperbolic space and a euclidean space, then it must be virtually nilpotent. We deduce that an amenable group regularly embeds…

We prove that for any infinite countable amenable group $G$, any $\epsilon > 0$ and any finite subset $K\subset G$, there exists a tiling (partition of $G$ into finite "tiles" using only finitely many "shapes"), where all the tiles are $(K;…

We establish a characterization of amenability for general Hausdorff topological groups in terms of matchings with respect to finite uniform coverings. Furthermore, we prove that it suffices to just consider two-element uniform coverings.…

It is shown that for a locally compact group $G$, if $L^{1}(G)^{**}$ is approximately weakly amenable, then $M(G)$ is approximately weakly amenable. Then, new notions of approximate weak amenability and approximate cyclic amenability for…

Moore characterized the amenability of automorphism groups of countable ultrahomogeneous structures by a Ramsey-type property. We extend this result to automorphism groups of metric Fra\"iss\'e structures, which encompass all Polish groups.…

Recall that a definable group is `definably amenable' if it admits a translation-invariant Keisler measure. We prove a combinatorial characterization of definable amenability for groups definable in NIP theories. More specifically, given a…