Property (T) and rigidity for actions on Banach spaces

Details Property (T) and rigidity for actions on Banach spaces Property (T) and rigidity for actions on Banach spaces

2005-06-17

arxiv.org/abs/math/0506361v2

See final version in: Acta Math 198 No. 1 (2007) 57--105

Mathematics

Group Theory

Many minor improvements

Scientific paper

10.1007/s11511-007-0013-0

We study property (T) and the fixed point property for actions on $L^p$ and other Banach spaces. We show that property (T) holds when $L^2$ is replaced by $L^p$ (and even a subspace/quotient of $L^p$), and that in fact it is independent of $1\leq p<\infty$. We show that the fixed point property for $L^p$ follows from property (T) when $1

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