Kazhdan’s property (𝑇) with respect to non-commutative 𝐿_{𝑝}-spaces

Olivier, Baptiste

doi:10.1090/S0002-9939-2012-11481-9

Kazhdan’s property $(T)$ with respect to non-commutative $L_{p}$-spaces
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by Baptiste Olivier

Proc. Amer. Math. Soc. 140 (2012), 4259-4269

DOI: https://doi.org/10.1090/S0002-9939-2012-11481-9

Published electronically: April 19, 2012

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Abstract:

We show that a group with Kazhdan’s property $(T)$ has property $(T_{B})$ for $B$ the Haagerup non-commutative $L_{p}(\mathcal {M})$-space associated with a von Neumann algebra $\mathcal {M}$, $1<p<\infty$. We deduce that higher rank groups have property $F_{L_{p}(\mathcal {M})}$.

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