Noncommutative maximal ergodic theorems

Details Noncommutative maximal ergodic theorems Noncommutative maximal ergodic theorems

2005-05-14

arxiv.org/abs/math/0505308v2

Mathematics

Operator Algebras

This is a revised version with minor modifications. To appear in J. Amer. Math. Soc

Scientific paper

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.

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