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Journal of the American Mathematical Society

Published by the American Mathematical Society, the Journal of the American Mathematical Society (JAMS) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6834 (online) ISSN 0894-0347 (print)

The 2020 MCQ for Journal of the American Mathematical Society is 4.79.

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Noncommutative maximal ergodic theorems
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by Marius Junge and Quanhua Xu PDF
J. Amer. Math. Soc. 20 (2007), 385-439 Request permission

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
  • 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