2951 articles  [english version]
 HAL : hal-00003557, version 1
 arXiv : math.OA/0412253
 Probability Theory and Related Fields 135 (2006) 520-546
 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.