Approximation properties for noncommutative $L^p$-spaces of high rank lattices and nonembeddability of expanders

Tim de Laat, Mikael de la Salle

This article contains two rigidity type results for $\mathrm{SL}(n,\mathbb{Z})$ for large $n$ that share the same proof. Firstly, we prove that for every $p\in [1,\infty ]$ differe…