Noncommutative maximal ergodic theorems
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- by Marius Junge and Quanhua Xu;
- J. Amer. Math. Soc. 20 (2007), 385-439
- DOI: https://doi.org/10.1090/S0894-0347-06-00533-9
- Published electronically: May 18, 2006
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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.References
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Bibliographic Information
- Marius Junge
- Affiliation: Department of Mathematics, University of Illinois, 1409 West Green Street, Urbana, Illinois 61801
- MR Author ID: 292431
- Email: junge@math.uiuc.edu
- Quanhua Xu
- Affiliation: Laboratoire de Mathématiques, Université de Franche-Comté, 16 rue de Gray, 25030 Besançon, Cedex, France
- MR Author ID: 232752
- Email: qx@math.univ-fcomte.fr
- 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
- © Copyright 2006
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: J. Amer. Math. Soc. 20 (2007), 385-439
- MSC (2000): Primary 46L53, 46L55; Secondary 46L50, 37A99
- DOI: https://doi.org/10.1090/S0894-0347-06-00533-9
- MathSciNet review: 2276775