Property (T) and rigidity for actions on Banach spaces

@article{Bader2007PropertyA,
  title={Property (T) and rigidity for actions on Banach spaces},
  author={U. Bader and A. Furman and T. Gelander and N. Monod},
  journal={Acta Mathematica},
  year={2007},
  volume={198},
  pages={57-105}
}
We study property (T) and the fixed-point property for actions on Lp and other Banach spaces. We show that property (T) holds when L2 is replaced by Lp (and even a subspace/quotient of Lp), and that in fact it is independent of 1≤p<∞. We show that the fixed-point property for Lp follows from property (T) when 1<p< 2+ε. For simple Lie groups and their lattices, we prove that the fixed-point property for Lp holds for any 1< p<∞ if and only if the rank is at least two. Finally, we obtain a… Expand