D ec 2 00 6 PROPERTY ( T ) AND RIGIDITY FOR ACTIONS ON BANACH SPACES
نویسندگان
چکیده
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 ≤ p < ∞. We show that the fixed point property for L p follows from property (T) when 1 < p < 2 + ε. For simple Lie groups and their lattices, we prove that the fixed point property for L p holds for any 1 < p < ∞ 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 spaces.
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ar X iv : m at h / 05 06 36 1 v 1 [ m at h . G R ] 1 7 Ju n 20 05 PROPERTY ( T ) AND RIGIDITY FOR ACTIONS ON BANACH SPACES
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 ≤ p < ∞. We show that the fixed point property for L p follows from property (T) when 1 < p < 2 + ε. For simple Lie groups and their lattices, we prove that the fi...
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