On ergodic theorems for free group actions on noncommutative spaces

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dc.creatorAnantharaman-Delaroche, Claire
dc.date2004-12-13
dc.date.accessioned2026-07-07T06:29:21Z
dc.date.available2026-07-07T06:29:21Z
dc.descriptionWe extend in a noncommutative setting the individual ergodic theorem of Nevo and Stein concerning measure preserving actions of free groups and averages on spheres $s_{2n}$ of even radius. Here we study state preserving actions of free groups on a von Neumann algebra $A$ and the behaviour of $(s_{2n}(x))$ for $x$ in noncommutative spaces $L^p(A)$. For the Cesàro means $\frac{1}{n}\sum_{k=0}^{n-1} s_k$ and $p = +\infty$, this problem was solved by Walker. Our approach is based on ideas of Bufetov. We prove a noncommutative version of Rota ``Alternierende Verfahren'' theorem. To this end, we introduce specific dilations of the powers of some noncommutative Markov operators.
dc.identifierhttps://arxiv.org/abs/math/0412253
dc.identifierhttp://arxiv.org/abs/math/0412253
dc.identifierProbability Theory and Related Fields 135 (2006) 520-546
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/98000
dc.subjectOperator Algebras
dc.subject46L53, 46L55, 46L50
dc.titleOn ergodic theorems for free group actions on noncommutative spaces
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