Related papers: Permanence of approximation properties for discret…

We study stability properties of amenable locally compact quantum groups under the bicrossed product construction. We obtain as our main result an equivalence between amenability of the bicrossed product and amenability of the matched…

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,…

The Haagerup property, which is a strong converse of Kazhdan's property $(T)$, has translations and applications in various fields of mathematics such as representation theory, harmonic analysis, operator K-theory and so on. Moreover, this…

We prove a weak form of the mean ergodic theorem for actions of amenable locally compact quantum groups in the von Neumann algebra setting.

We first give simplified and corrected accounts of some results in \cite{PiRCP} on compactifications of pseudofinite groups. For instance, we use a classical theorem of Turing \cite{Turing} to give a simplified proof that any definable…

Let $G$ and $H$ be locally compact, second countable groups. Assume that $G$ acts in a measure class preserving way on a standard probability space $(X,\mu)$ such that $L^\infty(X,\mu)$ has an invariant mean and that there is a Borel…

The weak Haagerup property for locally compact groups and the weak Haagerup constant was recently introduced by the second author. The weak Haagerup property is weaker than both weak amenability introduced by Cowling and the first author…

We define a relative property A for a countable group with respect to a finite family of subgroups. Many characterizations for relative property A are given. In particular a relative bounded cohomological characterization shows that if a…

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…

A finite von Neumann algebra $\mathcal{M}$ with a faithful normal trace $% \tau $ has Haagerup's approximation property (relative to a von Neumann subalgebra $\mathcal{N}$) if there exists a net $(\phi_{\alpha})_{\alpha\in \Lambda}$ of…

We consider a class (convex set) of quantum states containing all finite rank states and infinite rank states with the sufficient rate of decreasing of eigenvalues (in particular, all Gaussian states). Quantum states from this class are…

We study amenability of affine algebras (based on the notion of almost-invariant finite-dimensional subspace), and apply it to algebras associated with finitely generated groups. We show that a group G is amenable if and only if its group…

We prove a mean ergodic theorem for amenable discrete quantum groups. As an application, we prove a Wiener type theorem for continuous measures on compact metrizable groups.

We prove a number of results linking properties of actions by compact groups (both quantum and classical) on Banach spaces, such as uniform continuity, spectrum finiteness and extensibility of the actions across several constructions.…

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 define and study a notion of free wreath product with amalgamation for compact quantum groups. These objects were already introduced in the case of duals of discrete groups under the name "free wreath products of pairs" in a previous…

We show that Property $\mathrm{(TTT)}$ is an obstruction to weak amenability with Cowling--Haagerup constant $1$. More precisely, if $G$ is a countable group and $H$ is an infinite subgroup of $G$ such that the pair $(G,H)$ has relative…

A topological group $G$ is extremely amenable if every continuous action of $G$ on a compact space has a fixed point. Using the concentration of measure techniques developed by Gromov and Milman, we prove that the group of automorphisms of…

In this work, we study groupoids and their approximation properties, generalizing both the definitions and some known results for the group case. More precisely, we introduce weak amenability for groupoids using the definition of the…

In this paper, we give another two characterizations of relative amenability on finite von Neumann algebras, one of which can be thought of as an analogue of injective operator systems. As an application, we prove a stable property of…