no. 5
Functional analysis/Dynamical systems
Mean ergodic theorem in symmetric spaces
[Théorème ergodique moyen dans les espaces symétriques]

Présenté par : Gilles Pisier

Sukochev, Fedor1 ; Veksler, Aleksandr2
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, Tome 355 (2017) no. 5, pp. 559-562.

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.

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.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2017.03.014
Sukochev, Fedor 1 ; Veksler, Aleksandr 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 
@article{CRMATH_2017__355_5_559_0,
     author = {Sukochev, Fedor and Veksler, Aleksandr},
     title = {Mean ergodic theorem in symmetric spaces},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {559--562},
     publisher = {Elsevier},
     volume = {355},
     number = {5},
     year = {2017},
     doi = {10.1016/j.crma.2017.03.014},
     language = {en},
     url = {http://www.numdam.org/articles/10.1016/j.crma.2017.03.014/}
}
TY  - JOUR
AU  - Sukochev, Fedor
AU  - Veksler, Aleksandr
TI  - Mean ergodic theorem in symmetric spaces
JO  - Comptes Rendus. Mathématique
PY  - 2017
SP  - 559
EP  - 562
VL  - 355
IS  - 5
PB  - Elsevier
UR  - http://www.numdam.org/articles/10.1016/j.crma.2017.03.014/
DO  - 10.1016/j.crma.2017.03.014
LA  - en
ID  - CRMATH_2017__355_5_559_0
ER  - 
%0 Journal Article
%A Sukochev, Fedor
%A Veksler, Aleksandr
%T Mean ergodic theorem in symmetric spaces
%J Comptes Rendus. Mathématique
%D 2017
%P 559-562
%V 355
%N 5
%I Elsevier
%U http://www.numdam.org/articles/10.1016/j.crma.2017.03.014/
%R 10.1016/j.crma.2017.03.014
%G en
%F CRMATH_2017__355_5_559_0
Sukochev, Fedor; Veksler, Aleksandr. Mean ergodic theorem in symmetric spaces. Comptes Rendus. Mathématique, Tome 355 (2017) no. 5, pp. 559-562. doi : 10.1016/j.crma.2017.03.014. http://www.numdam.org/articles/10.1016/j.crma.2017.03.014/

[1] Bennett, C.; Sharpley, R. Interpolation of Operators, Academic Press Inc., London, 1988

[2] Cornfeld, I.; Fomin, S.; Sinai, Y. Ergodic Theory, Springer-Verlag, 1982

[3] Dunford, N.; Schwartz, J. Linear Operators. Part 1: General Theory, Interscience Publishers, New York, London, 1958

[4] Krein, S.; Petunin, Y.; Semenov, E. Interpolation of Linear Operators, Transl. Math. Monogr., vol. 54, AMS, Providence, RI, USA, 1982

[5] Lord, S.; Sukochev, F.; Zanin, D. Singular Traces. Theory and Applications, De Gruyter Stud. Math., vol. 46, 2013

[6] Sukochev, F.; Zanin, D. Traces on symmetrically normed operator ideals, J. Reine Angew. Math., Volume 678 (2013), pp. 163-200

[7] Veksler, A.; Fedorov, A. Statistical ergodic theorems in non-separable symmetric spaces of functions, Sib. Math. J., Volume 29 (1989), pp. 183-185

[8] A. Veksler, A. Fedorov, Symmetric spaces and mean ergodic theorems for automorphisms and flows, Tashkent, Fan 2016, 168 p. (in Russian).

Cité par Sources :