On a Hölder covariant version of mean dimension

Antoine Gournay

doi:10.1016/j.crma.2009.10.014

Functional Analysis/Dynamical Systems

On a Hölder covariant version of mean dimension
[Sur une modification Hölder covariante de la dimension moyenne]

Présenté par : Mikhaël Gromov

Antoine Gournay ¹

¹ Department of Mathematics, Faculty of Science, Kyoto University, Kyoto 606-8502, Japan

Comptes Rendus. Mathématique, Volume 347 (2009) no. 23-24, pp. 1389-1392.

Résumé
Abstract

Soit Γ un groupe dénombrable infini qui agit naturellement sur $ℓ^{p} (Γ)$ . Nous introduisons une obstruction, proche de la dimension moyenne, au fait que $ℓ^{p} (Γ)$ et $ℓ^{q} (Γ)$ soit Hölder conjugués.

Let Γ be a infinite countable group which acts naturally on $ℓ^{p} (Γ)$ . We introduce a modification of mean dimension which is an obstruction for $ℓ^{p} (Γ)$ and $ℓ^{q} (Γ)$ to be Hölder conjugates.

Reçu le : 2009-02-24
Accepté le : 2009-10-15
Publié le : 2009-10-27

DOI : 10.1016/j.crma.2009.10.014

Affiliations des auteurs :

Antoine Gournay ¹

¹ Department of Mathematics, Faculty of Science, Kyoto University, Kyoto 606-8502, Japan

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     title = {On a {H\"older} covariant version of mean dimension},
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     doi = {10.1016/j.crma.2009.10.014},
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Antoine Gournay. On a Hölder covariant version of mean dimension. Comptes Rendus. Mathématique, Volume 347 (2009) no. 23-24, pp. 1389-1392. doi : 10.1016/j.crma.2009.10.014. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2009.10.014/

Bibliographie
Cité par

[1] Y. Benyamini; J. Lindenstrauss Geometric Nonlinear Functional Analysis, vol. 1, American Mathematical Society Colloquium Publications, vol. 48, American Mathematical Society, Providence, RI, 2000

[2] A. Gournay Width of $ℓ^{p}$ balls, 2008 (or p. 16; Houston J. Math., in press) | arXiv | HAL

[3] M. Gromov Topological invariants of dynamical systems and spaces of holomorphic maps. I, Math. Phys. Anal. Geom., Volume 2 (1999) no. 4, pp. 323-415

[4] E. Lindenstrauss; B. Weiss Mean topological dimension, Israel J. Math., Volume 115 (2000), pp. 1-24

[5] M. Tsukamoto Macroscopic dimension of the $l^{p}$ -ball with respect to the $l^{q}$ -norm, J. Math. Kyoto Univ., Volume 48 (2008) no. 2, pp. 445-454

Xianfeng Ma; Junqi Yang; Ercai Chen Mean topological dimension for random bundle transformations, Ergodic Theory and Dynamical Systems, Volume 39 (2019) no. 4, pp. 1020-1041 | DOI:10.1017/etds.2017.51 | Zbl:1409.37033
Shinichiroh Matsuo; Masaki Tsukamoto Brody curves and mean dimension, Journal of the American Mathematical Society, Volume 28 (2015) no. 1, pp. 159-182 | DOI:10.1090/s0894-0347-2014-00798-0 | Zbl:1307.32013
Shinichiroh Matsuo; Masaki Tsukamoto Instanton approximation, periodic ASD connections, and mean dimension, Journal of Functional Analysis, Volume 260 (2011) no. 5, pp. 1369-1427 | DOI:10.1016/j.jfa.2010.11.008 | Zbl:1217.58007

Cité par 3 documents. Sources : zbMATH

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