Noncommutative maximal ergodic theorems

Junge, Marius¹ ; Xu, Quanhua²

¹ Department of Mathematics, University of Illinois, 1409 West Green Street, Urbana, Illinois 61801
² Laboratoire de Mathématiques, Université de Franche-Comté, 16 rue de Gray, 25030 Besançon, Cedex, France

Journal of the American Mathematical Society, Tome 20 (2007) no. 2, pp. 385-439

Résumé

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.

Détail

DOI : 10.1090/S0894-0347-06-00533-9

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