Banach property (T) for $\mathrm{S}{\mathrm{L}}_{\mathrm{n}}(\mathbb{Z})$ and its applications

Izhar Oppenheim

We prove that a large family of higher rank simple Lie groups (including $\mathrm{S}{\mathrm{L}}_{\mathrm{n}}(\mathbb{R})$ for $n\ge 3$) and their lattices have Banach property (T) with respect to all sup…