An obstruction to ℓ^p-dimension

2012/07/05 by Nicolas Monod, Monod, Nicolas, Henrik Densing Petersen +1
Mathematics · #FOS: Mathematics #Functional Analysis (math.FA) #Group Theory (math.GR) #math.FA #math.GR

paper · pdf · doi:10.48550/arxiv.1207.1199

5 pages (cosmetic changes wrt v1)

arxiv created 2012/07/13 · arxiv updated 2012/07/16

Abstract

For any group G containing an infinite elementary amenable subgroup, and any 2<p<∞, there exists closed invariant subspaces E_i\nearrow ℓ^pG and F≠ 0 such that E_i∩ F = 0 for all i. This is an obstacle to ℓ^p-dimension and gives a negative answer to a question of Gaboriau.

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