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# Noncommutative maximal ergodic theorems

Abstract : 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.
Document type :
Journal articles
Domain :

https://hal.archives-ouvertes.fr/hal-00477047
Contributor : Quanhua Xu Connect in order to contact the contributor
Submitted on : Tuesday, April 27, 2010 - 10:55:16 PM
Last modification on : Thursday, January 13, 2022 - 12:00:02 PM

### Citation

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

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