Related papers: On Amenable and Coamenable Coideals

Beyond the locally compact case, equivalent notions of amenability diverge, and some properties no longer hold, for instance amenability is not inherited by topological subgroups. This investigation is guided by some amenability-type…

Let $K$ be a commutative compact hypergroup and $L^1(K)$ the hypergroup algebra. We show that $L^1(K)$ is amenable if and only if $\pi_K$, the Plancherel weight on the dual space $\widehat{K}$, is bounded. Furthermore, we show that if $K$…

We consider the amenability of groupoids $G$ equipped with a group valued cocycle $c:G\to Q$ with amenable kernel $c^{-1}(e)$. We prove a general result which implies, in particular, that $G$ is amenable whenever $Q$ is amenable and if…

A topological group $G$ is called extremely amenable if every continuous action of $G$ on a compact space has a fixed point. This concept is linked with geometry of high dimensions (concentration of measure). We show that a von Neumann…

We analyze the dichotomy amenable/paradoxical in the context of (discrete, countable, unital) semigroups and corresponding semigroup rings. We consider also F{\o}lner's type characterizations of amenability and give an example of a…

Let G be a locally compact group, and let A(G) and B(G) denote its Fourier and Fourier-Stieltjes algebras. These algebras are dual objects of the group and measure algebras, L^1(G) and M(G), in a sense which generalizes the Pontryagin…

We define a Banach algebra A to be dual if $A = (A_\ast)^\ast$ for a closed submodule $A_\ast$ of $A^\ast$. The class of dual Banach algebras includes all $W^\ast$-algebras, but also all algebras M(G) for locally compact groups G, all…

We prove that amenability of a discrete group is equivalent to dimension flatness of certain ring inclusions naturally associated with measure preserving actions of the group. This provides a group-measure space theoretic solution to a…

Let G be a locally compact group, and ZL1(G) be the centre of its group algebra. We show that when $G$ is compact ZL1(G) is not amenable when G is either nonabelian and connected, or is a product of infinitely many finite nonabelian groups.…

In this note, we prove that a semigroup $S$ is left amenable if and only if every two nonzero elements of $\ell^1_+(S)$ have a common nonzero right multiple, where $\ell^1_+(S)$ is the positive part of the Banach algebra $\ell^1(S)$, or…

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…

We initiate a quantitative study of measure equivalence (and orbit equivalence) between finitely generated groups, which extends the classical setting of $\mathrm L^p$ measure equivalence. In this paper, our main focus will be on amenable…

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…

Let A be a Banach algebra and I be a closed ideal of A. We say that A is amenable relative to I, if A/I is an amenable Banach algebra. We study the relative amenability of Banach algebras and investigate the relative amenability of…

We show that the groups of finite energy loops and paths (that is, those of Sobolev class $H^1$) with values in a compact connected Lie group, as well as their central extensions, satisfy an amenability-like property: they admit a…

Given a countable residually finite group, we construct a compact group K and two elements w and u of K with the following properties: The group generated by w and the cube of u is amenable, the group generated by w and u contains a copy of…

For a locally compact group $G$, let $A(G)$ denote its Fourier algebra and $\hat{G}$ its dual object, i.e. the collection of equivalence classes of unitary represenations of $G$. We show that the amenability constant of $A(G)$ is less than…

We examine the question of quasidiagonality for C*-algebras of discrete amenable groups from a variety of angles. We give a quantitative version of Rosenberg's theorem via paradoxical decompositions and a characterization of…

A new flavour of amenability for discrete semigroups is proposed that generalises group amenability and follows from a \Folner-type condition. Some examples are explored, to argue that this new notion better captures some essential ideas of…

We revisit Gersten's $\ell^\infty$-cohomology of groups and spaces, removing the finiteness assumptions required by the original definition while retaining its geometric nature. Mirroring the corresponding results in bounded cohomology, we…