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Université d'Orléans |  |
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Université d'Orléans | |
| HAL : hal-00003557, version 1 |
| arXiv : math.OA/0412253 |
| Fiche détaillée |  Récupérer au format |
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| Probability Theory and Related Fields 135 (2006) 520-546 |
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| On ergodic theorems for free group actions on noncommutative spaces |
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| Claire Anantharaman-Delaroche 1 |
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| (2006) |
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| We 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. |
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| 1 : | Mathématiques - Analyse, Probabilités, Modélisation - Orléans (MAPMO) |
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Université d'Orléans – CNRS : UMR7349 |
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| Domaine | : | Mathématiques/Algèbres d'opérateurs |
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| Noncommutative ergodic theorems – free group actions |
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| hal-00003557, version 1 | |
| http://hal.archives-ouvertes.fr/hal-00003557 | |
| oai:hal.archives-ouvertes.fr:hal-00003557 | |
| Contributeur : Claire Anantharaman-Delaroche | |
| Soumis le : Lundi 13 Décembre 2004, 16:11:46 | |
| Dernière modification le : Vendredi 26 Mai 2006, 14:34:02 | |
