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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

   

 

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


Author: Baptiste Olivier
Journal: Proc. Amer. Math. Soc. 140 (2012), 4259-4269
MSC (2010): Primary 46L52
Published electronically: April 19, 2012
MathSciNet review: 2957217
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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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Additional Information

Baptiste Olivier
Affiliation: Institut de Recherche Mathématiques de Rennes, Université de Rennes 1, Rennes, France

DOI: http://dx.doi.org/10.1090/S0002-9939-2012-11481-9
Keywords: Haagerup non-commutative $L_{p}(\mathcal{M})$-spaces, property $(T)$, group representations, Mazur map, property $F_{L_{p}(\mathcal{M})}$.
Received by editor(s): February 7, 2011
Received by editor(s) in revised form: May 31, 2011
Published electronically: April 19, 2012
Communicated by: Marius Junge
Article copyright: © Copyright 2012 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.