Related papers: Characterisations for uniform amenability

In this paper, we characterize the amenablity of locally compact groups in terms of the properties of the Orlicz Figa-Talamanca Herz algebras.

We study definably amenable NIP groups. We develop a theory of generics, showing that various definitions considered previously coincide, and study invariant measures. Applications include: characterization of regular ergodic measures, a…

We show that the amenability of a locally compact group $G$ is equivalent to a factorization property of $VN(G)$ which is given by $ VN(G) = <VN(G)^*VN(G)>$. This answer partially two problems proposed by Z. Hu and M. Neufang in their…

We study a generalization of conditional probability for arbitrary ordered vector spaces. A related problem is that of assigning a numerical value to one vector relative to another. We characterize the groups for which these generalized…

This paper concerns the study of regular Fourier hypergroups through multipliers of their associated Fourier algebras. We establish hypergroup analogues of well-known characterizations of group amenability, introduce a notion of weak…

In Functional Analysis, certain conclusions apply to sequences, but they cannot be carried over when we consider nets. In fact, some nets, including sequences, can behave unexpectedly. In this paper we are interested in exploring the…

In 2005, Abdollahi and Rejali, studied the relations between paradoxical decompositions and configurations for semigroups. In the present paper, we introduce another concept of amenability on semigroups and groups which includes amenability…

The aim of this brief note is to offer another proof of a theorem of Hrushovski that approximate subgroups of GL_n(C) are almost nilpotent. This approach generalizes to uniformly non amenable groups.

We show that a finitely generated soluble group is virtually nilpotent if and only if the diameter of its finite coset spaces admits a uniform polynomial lower bound in terms of their size. We obtain the same conclusion for certain finitely…

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…

Given a locally compact quantum group $\mathbb{G}$ and a closed quantum subgroup $\mathbb{H}$, we show that $\mathbb{G}$ is amenable if and only if $\mathbb{H}$ is amenable and $\mathbb{G}$ acts amenably on the quantum homogenous space…

In this note we extend two characterizations of admissible operators with respect to $\mathrm{L}^p$ to more general Orlicz spaces. The equivalent conditions are given by the property that an associated operator generates a strongly…

We prove an inverse theorem for the Gowers $U^2$-norm for maps $G\to\mathcal M$ from an countable, discrete, amenable group $G$ into a von Neumann algebra $\mathcal M$ equipped with an ultraweakly lower semi-continuous, unitarily invariant…

We show that the topology of pointwise convergence on scattered spaces is compatible with the group structure of their homeomorphism group. We then establish a few topological properties of the homeomorphism group of the first uncountable…

We introduce a topological property for finitely generated groups called stackable that implies the existence of an inductive procedure for constructing van Kampen diagrams with respect to a particular finite presentation. We also define…

Amenable category is a variant of the Lusternik-Schnirelman category, based on covers by amenable open subsets. We study the monotonicity problem for degree-one maps and amenable category and the relation between amenable category and…

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…

Let G be a locally compact abelian group, $\omega:G\to (0,\infty)$ be a weight, and ($\Phi$,$\Psi$) be a complementary pair of strictly increasing continuous Young functions. We show that for the weighted Orlicz algebra $L^\Phi_\omega(G)$,…

If matrices almost satisfying a group relation are close to matrices exactly satisfying the relation, then we say that a group is matricially stable. Here "almost" and "close" are in terms of the Hilbert-Schmidt norm. Using tracial 2-norm…

It is argued that universality is severely limited for models with multiple fixed points. As a demonstration the renormalization group equations are presented for the potential and the wave function renormalization constants in the $O(N)$…