no. 23-24
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, Antoine1
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

Let Γ be a infinite countable group which acts naturally on ℓp(Γ). We introduce a modification of mean dimension which is an obstruction for ℓp(Γ) and ℓq(Γ) to be Hölder conjugates.

Soit Γ un groupe dénombrable infini qui agit naturellement sur ℓp(Γ). Nous introduisons une obstruction, proche de la dimension moyenne, au fait que ℓp(Γ) et ℓq(Γ) soit Hölder conjugués.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2009.10.014

Gournay, Antoine 1

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

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[2] Gournay, A. Width of ℓp 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

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[5] Tsukamoto, M. Macroscopic dimension of the lp-ball with respect to the lq-norm, J. Math. Kyoto Univ., Volume 48 (2008) no. 2, pp. 445-454

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