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Nicolas Monod; Henrik Densing Petersen
An obstruction to $\ell ^{p}$-dimension
(Un obstacle à la dimension $\ell ^{p}$)
Annales de l'institut Fourier, 64 no. 4 (2014), p. 1363-1371, doi: 10.5802/aif.2883
Article PDF | Reviews MR 3329666 | Zbl 06387310
Class. Math.: 43A15
Keywords: $\ell ^p$-dimension, abstract harmonic analysis

Résumé - Abstract

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

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