Almost uniform convergence in the noncommutative Dunford–Schwartz ergodic theorem

Semyon Litvinov

doi:10.1016/j.crma.2017.09.014

Functional analysis

Almost uniform convergence in the noncommutative Dunford–Schwartz ergodic theorem
[Convergence presque uniforme dans le théorème ergodique de Dunford–Schwartz non commutatif]

Présenté par : the Editorial Board

Semyon Litvinov ¹

¹ 76 University Drive, Pennsylvania State University, Hazleton 18202, United States

Comptes Rendus. Mathématique, Volume 355 (2017) no. 9, pp. 977-980.

Résumé
Abstract

Cette Note donne une réponse positive à la question suivante : les moyennes de Cesáro ergodiques engendrées par un opérateur de Dunford–Schwartz dans un espace non commutatif $L^{p} (M, τ)$ , $1 \leq p < \infty$ , convergent-elles presque uniformément (au sens d'Egorov) ? Ce problème remonte au texte original de Yeadon [21], publié en 1977, dans lequel la convergence presque uniforme bilatérale de ces moyennes est établie pour $p = 1$ .

This article gives an affirmative solution to the problem whether the ergodic Cesáro averages generated by a positive Dunford–Schwartz operator in a noncommutative space $L^{p} (M, τ)$ , $1 \leq p < \infty$ , converge almost uniformly (in Egorov's sense). This problem goes back to the original paper of Yeadon [21], published in 1977, where bilaterally almost uniform convergence of these averages was established for $p = 1$ .

Reçu le : 2017-06-29
Accepté le : 2017-09-20
Publié le : 2017-09-01

DOI : 10.1016/j.crma.2017.09.014

Affiliations des auteurs :

Semyon Litvinov ¹

¹ 76 University Drive, Pennsylvania State University, Hazleton 18202, United States

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Semyon Litvinov. Almost uniform convergence in the noncommutative Dunford–Schwartz ergodic theorem. Comptes Rendus. Mathématique, Volume 355 (2017) no. 9, pp. 977-980. doi : 10.1016/j.crma.2017.09.014. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2017.09.014/

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