Related papers: Mean topological dimension of induced amenable gro…

In this manuscript, we focus on the investigation of the BS dimension and BS packing dimension under amenable group actions. Firstly, we obtain a Bowen's equation which illustrate the relation of BS packing dimension to the packing…

In this paper we generalize Kingman's sub-additive ergodic theorem to a large class of infinite countable discrete amenable group actions.

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…

For a topological group $G$, amenability can be characterized by the amenability of the convolution Banach algebra $L^1(G)$. Here a Banach algebra $A$ is called amenable if every bounded derivation from $A$ into any dual--type…

For every infinite (countable discrete) amenable group $G$ and every positive integer $d$ we construct a minimal $G$-action of mean dimension $d/2$ which cannot be embedded in the full $G$-shift on $([0,1]^d)^G$.

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…

We find limits of some multiple ergodic averages, generalizing a result of Bergelson to the setting of two commuting transformations and actions of amenable groups.

In this paper we study analogues of amenability for topological groups in the context of definable structures. We prove fixed point theorems for such groups. More importantly, we propose definitions for definable actions and continuous…

In this short note, for countably infinite amenable group actions, we provide topological proofs for the following results: Bowen topological entropy (dimensional entropy) of the whole space equals the usual topological entropy along…

In this paper, among other things, we state and prove the mean ergodic theorem for amenable semigroup algebras.

Let $G$ be an infinite countable amenable group and $P$ a polyhedron with topological dimension $dim(P)<\infty$. We construct a minimal subshift $(X,G)$ such that its mean topological dimension is equal to $dim(P)$. This result answers the…

We unify and extend some previous results about cubic ergodic averages and sets of positive density in products of groups. This provides a joint generalization of earlier work of the author in the case of two commuting actions of an…

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…

In the current paper we attempt to transfer the notion of the projectional entropy, originally defined for multidimensional subshifts, to the case of actions of amenable groups. The main theorem states that if a system is strongly…

We extend F{\o}lner's amenability criterion to the realm of general topological groups. Building on this, we show that a topological group $G$ is amenable if and only if its left translation action can be approximated in a uniform manner by…

This text surveys classical and recent results in the field of amenability of groups, from a combinatorial standpoint. It has served as the support of courses at the University of G\"ottingen and the \'Ecole Normale Sup\'erieure. The goals…

We introduce an invariant, called mean rank, for any module M of the integral group ring of a discrete amenable group $\Gamma$, as an analogue of the rank of an abelian group. It is shown that the mean dimension of the induced…

We investigate the notion of relatively amenable topological action and show that the action of Thompson's group $T$ on $S^1$ is relatively amenable with respect to Thompson's group $F$. We use this to conclude that $F$ is exact if and only…

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 introduce and study various notions of amenability continuous (Borel) partial actions of locally compact (Borel) groups $G$ on topological (standard Borel) spaces. We also study amenability of partial representations of a locally compact…