Noncommutative maximal ergodic theorems

Marius Junge; Quanhua Xu

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arXiv · math/0505308

Noncommutative maximal ergodic theorems

Marius Junge·Quanhua Xu

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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.

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BibTeX RIS

Marius Junge, Quanhua Xu. 2006-03-08. Noncommutative maximal ergodic theorems. https://arxiv.org/abs/math/0505308

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