Pointwise ergodic theorems beyond amenable groups

DOI10.1017/S0143385712000041zbMath1276.37002arXiv1103.2519OpenAlexW2963699685MaRDI QIDQ4928749

Amos Nevo, Lewis Phylip Bowen

Publication date: 18 June 2013

Published in: Ergodic Theory and Dynamical Systems (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1103.2519

zbMATH Keywords

latticeamenable groupsFølner sequencessemi-simple Lie groupsamenable actionpointwise ergodic theoremsmaximal ergodic theoremstempered Følner sequencesstable type \(\mathrm{III}_{\lambda}\)stable type \(\mathrm{III}_1\)

Mathematics Subject Classification ID

Ergodic theorems, spectral theory, Markov operators (37A30) Means on groups, semigroups, etc.; amenable groups (43A07) General groups of measure-preserving transformations and dynamical systems (37A15)

Related Items (17)

An alternative definition of topological entropy for amenable group actions ⋮ FAILURE OF THE POINTWISE AND MAXIMAL ERGODIC THEOREMS FOR THE FREE GROUP ⋮ The Katok's entropy formula for amenable group actions ⋮ A horospherical ratio ergodic theorem for actions of free groups ⋮ Charmenability of higher rank arithmetic groups ⋮ Noncommutative ergodic theory of higher rank lattices ⋮ Shannon-McMillan-Breiman theorem along almost geodesics in negatively curved groups ⋮ The type and stable type of the boundary of a Gromov hyperbolic group ⋮ Bowen topological entropy of subsets for amenable group actions ⋮ Bernoulli actions of type \(\mathrm{III}_{1}\) and \(L^2\)-cohomology ⋮ Sub-additive ergodic theorems for countable amenable groups ⋮ On the \(K\) property for Maharam extensions of Bernoulli shifts and a question of Krengel ⋮ Bi-exact groups, strongly ergodic actions and group measure space type III factors with no central sequence ⋮ Ergodic theorems for the shift action and pointwise versions of the Abért-Weiss theorem ⋮ A variational principle of topological pressure on subsets for amenable group actions ⋮ The Shannon-McMillan-Breiman theorem beyond amenable groups ⋮ Amenable equivalence relations and the construction of ergodic averages for group actions

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