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 s 2 n of even radius. Here we study state preserving actions of free groups on a von Neumann algebra A and the behaviour of (s 2 n (x)) for x in noncommutative spaces L p (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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