research
Property (T) and rigidity for actions on Banach spaces
Abstract
We study property (T) and the fixed point property for actions on and other Banach spaces. We show that property (T) holds when is replaced by (and even a subspace/quotient of ), and that in fact it is independent of . We show that the fixed point property for follows from property (T) when 1. For simple Lie groups and their lattices, we prove that the fixed point property for holds for any if and only if the rank is at least two. Finally, we obtain a superrigidity result for actions of irreducible lattices in products of general groups on superreflexive Banach spaces.Comment: Many minor improvement