An obstruction to p -dimension  [ Un obstacle à la dimension p  ]
Annales de l'Institut Fourier, Tome 64 (2014) no. 4, p. 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 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  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 p G by closed invariant subspaces which all intersect trivially a fixed non-trivial closed invariant subspace. This is an obstacle to p -dimension and gives an answer to a question of Gaboriau.
Reçu le : 2013-01-30
Révisé le : 2014-02-04
Accepté le : 2014-06-13
DOI : https://doi.org/10.5802/aif.2883
Classification:  43A15
Mots clés: dimension p , analyse harmonique abstraite
@article{AIF_2014__64_4_1363_0,
     author = {Monod, Nicolas and Petersen, Henrik Densing},
     title = {An obstruction to $\ell ^{p}$-dimension},
     journal = {Annales de l'Institut Fourier},
     publisher = {Association des Annales de l'institut Fourier},
     volume = {64},
     number = {4},
     year = {2014},
     pages = {1363-1371},
     doi = {10.5802/aif.2883},
     zbl = {06387310},
     mrnumber = {3329666},
     language = {en},
     url = {https://aif.centre-mersenne.org/item/AIF_2014__64_4_1363_0}
}
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/item/AIF_2014__64_4_1363_0/

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