no. 4
An obstruction to ℓ p -dimension
[Un obstacle à la dimension ℓ p ]
Monod, Nicolas1 ; Petersen, Henrik Densing2
1 École Polytechnique Fédérale de Lausanne Station 8, CH-1015 Lausanne (Switzerland)
2 University of Copenhagen Department of Mathematical Sciences Universitetsparken 5 2100 København Ø(Denmark)
Annales de l'Institut Fourier, Tome 64 (2014) no. 4, pp. 1363-1371.

Soit G un groupe contenant un sous-groupe infini élémentairement moyennable et soit 2<p<∞. Nous construisons des sous-G-modules fermés de ℓ p G d’union croissante dense mais qui rencontrent trivialement un sous-module fermé non trivial. Ce phénomène est un obstacle à la quête d’une dimension ℓ p et répond à une question de Gaboriau.

Let G be any group containing an infinite elementary amenable subgroup and let 2<p<∞. We construct an exhaustion of ℓ p G by closed invariant subspaces which all intersect trivially a fixed non-trivial closed invariant subspace. This is an obstacle to ℓ p -dimension and gives an answer to a question of Gaboriau.

DOI : 10.5802/aif.2883
Classification : 43A15
Keywords: $\ell ^p$-dimension, abstract harmonic analysis
Mot clés : dimension $\ell ^p$, analyse harmonique abstraite

Monod, Nicolas 1 ; Petersen, Henrik Densing 2

1 École Polytechnique Fédérale de Lausanne Station 8, CH-1015 Lausanne (Switzerland)
2 University of Copenhagen Department of Mathematical Sciences Universitetsparken 5 2100 København Ø(Denmark) 
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Monod, Nicolas; Petersen, Henrik Densing. An obstruction to $\ell ^{p}$-dimension. Annales de l'Institut Fourier, Tome 64 (2014) no. 4, pp. 1363-1371. doi : 10.5802/aif.2883. https://aif.centre-mersenne.org/articles/10.5802/aif.2883/

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