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Noncommutative maximal ergodic theorems

Authors: Marius Junge and Quanhua Xu
Journal: J. Amer. Math. Soc. 20 (2007), 385-439
MSC (2000): Primary 46L53, 46L55; Secondary 46L50, 37A99
Published electronically: May 18, 2006
MathSciNet review: 2276775
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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 von Neumann algebra theory and in quantum probability.

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Additional Information

Marius Junge
Affiliation: Department of Mathematics, University of Illinois, 1409 West Green Street, Urbana, Illinois 61801

Quanhua Xu
Affiliation: Laboratoire de Mathématiques, Université de Franche-Comté, 16 rue de Gray, 25030 Besançon, Cedex, France

Keywords: Noncommutative $L_p$-spaces, maximal ergodic theorems, individual ergodic theorems
Received by editor(s): March 5, 2005
Published electronically: May 18, 2006
Additional Notes: The first author was partially supported by the National Science Foundation grant DMS-0301116
Article copyright: © Copyright 2006 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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