An obstruction to ${\ell }^p$-dimension

Abstract

For any group $G$ containing an infinite elementary amenable subgroup, and any $2<p<\infty$, there exists closed invariant subspaces $E_i\nearrow {\ell }^{p}G$ and $F\ne 0$ such that $E_i\cap F=0$ for all $i$. This is an obstacle to ${\ell }^p$-dimension and gives a negative answer to a question of Gaboriau.

5 pages (cosmetic changes wrt v1)