Relative Property (T) for Topological Groups


In this paper, we investigate Kazhdan’s relative Property (T) for pairs , where is a topological group and is any subset of . We show that the pair has Property (FH) and every function conditionally of negative type on is X-bounded if the pair has relative Property (T). We also prove that has Property (T) whenis a s -compact locally compact group generated by its subgroups and the pair has relative Property (T) for all .

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Tao, J. and Yan, W. (2014) Relative Property (T) for Topological Groups. Applied Mathematics, 5, 2988-2993. doi: 10.4236/am.2014.519285.

Conflicts of Interest

The authors declare no conflicts of interest.


[1] Kekka, B., Harpe, P.D.L. and Valette, A. (2008) Kazhdan’s Property T. Cambridge University Press, Cambridge.
[2] Chifan, I. and Ioana, A. (2011) On Relative Property (T) and Haagerup’s Property. Transactions of the American Mathematical Society, 363, C6407-C6420.
[3] Cornulier, Y. (2006) Relative Kazhdan Property. Annales Scientifiques de1’école Hormale Supérieure, 39, 301-333.
[4] Ershov, M. and Jaikin-Zapirain, A. (2010) Property (T) for Noncommutative Universal Lattices. Inventiones Mathematicae, 179, 303-347.
[5] Kazhdan, D. (1967) Connection of Dual Space of Group with the Structure of Its Closed Subgroups. Functional Analysis and Its Applications, 1, 63-65.
[6] Margulis, G. (1982) Finitely-Additive Invariant Measures on Euclidean Spaces. Ergodic Theory and Dynamical Systems, 2, 383-396.
[7] Harpe, P.D.L., Valette, A. and Marc, B. (1989) La Propriété (T) de Kazhdan pour les groups localement compacts. Astérisque 175, Société mathématique de France (SMF).
[8] Shalom, Y. (1999) Bounded Generation and Kazhdan’s Property (T). Publications Mathématiques de l’Institut des Hautes études Scientifiques, 90, 145-168.
[9] Jolissaint, P. (2005) On Property (T) for Pairs of Topological Groups. L’Enseignement Mathématique, 51, 31-45.

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