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An obstruction to ℓ p -dimension

Nicolas Monod;  Henrik Densing Petersen — 2014

Annales de l’institut Fourier

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.

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