Related papers: A mean ergodic theorem for actions of amenable qua…
In his study of amenable unitary representations, M. E. B. Bekka asked if there is an analogue for such representations of the remarkable fixed-point property for amenable groups. In this paper, we prove such a fixed-point theorem in the…
We prove pointwise and maximal ergodic theorems for probability measure preserving (p.m.p.) actions of any countable group, provided it admits an essentially free, weakly mixing amenable action of stable type $III_1$. We show that this…
The notion of compact quantum subgroup is revisited and an alternative definition is given. Induced representations are considered and a Frobenius reciprocity theorem is obtained. A relationship between ergodic actions of compact quantum…
We introduce inner amenability for discrete p.m.p. groupoids and investigate its basic properties, examples, and the connection with central sequences in the full group of the groupoid or central sequences in the von Neumann algebra…
Among the ergodic actions of a compact quantum group $\mathbb{G}$ on possibly non-commutative spaces, those that are {\it embeddable} are the natural analogues of actions of a compact group on its homogeneous spaces. These can be realized…
We study fluctuations of ergodic averages generated by actions of amenable groups. In the setting of an abstract ergodic theorem for locally compact second countable amenable groups acting on uniformly convex Banach spaces, we deduce a…
We introduce computable actions of computable groups and prove the following versions of effective Birkhoff's ergodic theorem. Let $\Gamma$ be a computable amenable group, then there always exists a canonically computable tempered two-sided…
We present a general new method for constructing pointwise ergodic sequences on countable groups, which is applicable to amenable as well as to non-amenable groups and treats both cases on an equal footing. The principle underlying the…
We prove a pointwise ergodic theorem and a maximal inequality for actions of amenable groups on noncommutative measure spaces. To do so, we establish a square function estimate quantifying the difference between ergodic averages and some…
We prove that amenability of a unitary co-representation $U$ of a locally compact quantum group passes to unitary co-representations that weakly contain $U$. This generalizes a result of Bekka, and answers affirmatively a question of…
We generalize the notion of weakly mixing unitary representations to locally compact quantum groups, introducing suitable extensions of all standard characterizations of weak mixing to this setting. These results are used to complement the…
We prove that every ergodic amenable action of an algebraic group over a local field of characteristic zero is induced from an ergodic action of an amenable subgroup.
In this article, we consider actions of \mathcal{Z}_+^d, \mathcal{R}_+^d and finitely generated free groups on a von Neumann algebras $M$ and prove a version of maximal ergodic inequality. Additionally, we establish non-commutative…
We study fluctuations of ergodic averages generated by actions of amenable groups. In the setting of an abstract ergodic theorem for locally compact second countable amenable groups acting on uniformly convex Banach spaces, we deduce a…
We prove that weak amenability of a locally compact group imposes a strong condition on its amenable closed normal subgroups. This extends non weak amenability results of Haagerup (1988) and Ozawa--Popa (2010). A von Neumann algebra…
We prove a version of ergodic theorem for an action of an amenable group, where a F{\o} lner sequence needs not to be tempered. Instead, it is assumed that a function satisfies certain mixing condition.
Given a locally compact quantum group $\mathbb{G}$ and an ergodic, integrable action $L^\infty(\mathbb{X})\stackrel{\alpha}\curvearrowleft \mathbb{G}$, the von Neumann algebra $L^\infty(\mathbb{X}\times_{\mathbb{G}}\bar{\mathbb{X}}):=…
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.
We show that a certain tiling property (which directly implies the pointwise ergodic theorem) holds for pmp actions of amenable groups along increasing Tempelman F{\o}lner sequences, thus providing a short and combinatorial proof of the…
We study mean ergodicity in amenable operator semigroups and establish the connection to the convergence of strong and weak ergodic nets. We then use these results in order to show the convergence of uniform families of ergodic nets that…