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

Presented by: 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.

Abstract
Résumé

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.

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.

Received: 2009-02-24
Accepted: 2009-10-15
Published online: 2009-10-27

DOI: 10.1016/j.crma.2009.10.014

Author's affiliations:

Antoine Gournay ¹

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

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     author = {Antoine Gournay},
     title = {On a {H\"older} covariant version of mean dimension},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {1389--1392},
     publisher = {Elsevier},
     volume = {347},
     number = {23-24},
     year = {2009},
     doi = {10.1016/j.crma.2009.10.014},
     language = {en},
}

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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/

References
Cited by

[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

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