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Article Dans Une Revue J. Amer. Math. Soc. Année : 2006

Noncommutative maximal ergodic theorems

Résumé

This paper is devoted to the study of various maximal ergodic theorems in noncommutative $L_p$-spaces. In particular, we prove the noncommutative analogue of the classical Dunford-Schwartz maximal ergodic inequality for positive contractions on $L_p$ and the analogue of Stein's maximal inequality for symmetric positive contractions. We also obtain the corresponding individual ergodic theorems. We apply these results to a family of natural examples which frequently appear in theory of von Neumann algebras and in quantum probability.

Dates et versions

hal-00477047 , version 1 (27-04-2010)

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Marius Junge, Quanhua Xu. Noncommutative maximal ergodic theorems. J. Amer. Math. Soc., 2006, 20, pp.385-439. ⟨hal-00477047⟩
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