On a Hölder covariant version of mean dimension

Gournay, Antoine

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

Gournay, Antoine ¹

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

Comptes Rendus. Mathématique, Tome 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 :

Gournay, Antoine 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},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {1389--1392},
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Gournay, Antoine. On a Hölder covariant version of mean dimension. Comptes Rendus. Mathématique, Tome 347 (2009) no. 23-24, pp. 1389-1392. doi : 10.1016/j.crma.2009.10.014. http://www.numdam.org/articles/10.1016/j.crma.2009.10.014/

Bibliographie
Cité par

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

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

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

[5] Tsukamoto, M. 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

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