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arXiv · 1207.1199

An obstruction to $\ell^p$-dimension

Nicolas Monod·Henrik Densing Petersen
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Abstract

For any group $G$ containing an infinite elementary amenable subgroup, and any $2<p<\infty$, there exists closed invariant subspaces $E_i\nearrow \ell^pG$ and $F\neq 0$ 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.

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Nicolas Monod, Henrik Densing Petersen. 2012-07-13. An obstruction to $\ell^p$-dimension. https://arxiv.org/abs/1207.1199

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