On ergodic theorems for free group actions on noncommutative spaces |
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Authors: | Claire Anantharaman-Delaroche |
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Institution: | (1) Départment de Mathématiques, Université d'Orléans, B. P. 6759, 45067 Orléans Cedex 2, France |
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Abstract: | 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 s2n of even radius. Here we study state preserving actions of free groups on a von Neumann algebra A and the behaviour of (s2n(x)) for x in noncommutative spaces Lp(A). For the Cesàro means 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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Keywords: | Primary 46L53 46L55 Secondary 46L50 |
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