Comptes Rendus
no. 5
Functional analysis/Dynamical systems
Mean ergodic theorem in symmetric spaces

Presented by: Gilles Pisier

Fedor Sukochev1; Aleksandr Veksler2
1 School of Mathematics and Statistics, University of New South Wales, Kensington, NSW, 2052, Australia
2 Institute of Mathematics, National University of Uzbekistan, Tashkent, Uzbekistan
Comptes Rendus. Mathématique, Volume 355 (2017) no. 5, pp. 559-562.

We investigate the validity of the Mean Ergodic Theorem in symmetric Banach function spaces E. The assertion of that theorem always holds when E is separable, whereas the situation is more delicate when E is non-separable. To describe positive results in the latter setting, we use the connections with the theory of singular traces.

Nous étudions la validité du théorème de la moyenne ergodique dans les espaces de fonctions symétriques E. Nous montrons que ce théorème est toujours vérifié lorsque E est séparable ; cependant, la situation est plus délicate dans le cas non séparable. Les résultats positifs obtenus dans ce cadre utilisent des connexions avec la théorie des traces singulières.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crma.2017.03.014

Fedor Sukochev 1; Aleksandr Veksler 2

1 School of Mathematics and Statistics, University of New South Wales, Kensington, NSW, 2052, Australia
2 Institute of Mathematics, National University of Uzbekistan, Tashkent, Uzbekistan 
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Fedor Sukochev; Aleksandr Veksler. Mean ergodic theorem in symmetric spaces. Comptes Rendus. Mathématique, Volume 355 (2017) no. 5, pp. 559-562. doi : 10.1016/j.crma.2017.03.014. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2017.03.014/

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