Noncommutative maximal ergodic theorems
Operator Algebras
2007-05-23 v2 Dynamical Systems
Functional Analysis
Abstract
This paper is devoted to the study of various maximal ergodic theorems in noncommutative -spaces. In particular, we prove the noncommutative analogue of the classical Dunford-Schwartz maximal ergodic inequality for positive contractions on 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.
Cite
@article{arxiv.math/0505308,
title = {Noncommutative maximal ergodic theorems},
author = {Marius Junge and Quanhua Xu},
journal= {arXiv preprint arXiv:math/0505308},
year = {2007}
}
Comments
This is a revised version with minor modifications. To appear in J. Amer. Math. Soc