For any group G containing an infinite elementary amenable subgroup, and any 2<p<∞, there exists closed invariant subspaces Ei ↑ ℓpG and F≠ 0 such that Ei∩ F = 0 for all i. This is an obstacle to ℓp-dimension and gives a negative answer to a question of Gaboriau.
Authors: N. Monod, H.D. Petersen