[math/0506361] Property (T) and rigidity for actions on Banach spaces

[math/0506361] Property (T) and rigidity for actions on Banach spaces

Here the authors study variations of property T for actions on Banach spaces, especially Lp. When p is not 2 the equivalence between the original version of property T (isolation of the trivial representation) and the fixed point version F (affine isometric actions) does not hold.
They prove that every property T group has T(L^p) for all p, and F(L^p) for p<2+\epsilon.