Property (T) for C*-dynamical systems

Document Type: Research Paper


1 Department of Mathematics, Azarbaijan Shahid Madani University, Tabriz, Islamic Republic of Iran.

2 Faculty of Sciences, Sahand University of Technology, Tabriz, Islamic Republic of Iran.


In this paper, we introduce a notion of property (T) for a C- dynamical system (A, G, α) consisting of a unital C-algebra A, a locally compact group G, and an action α on A. As a result, we show that if A has strong property (T) and G has Kazhdan’s property (T), then the triple (A, G, α) has property (T).


[1] M. B. Bekka, Property (T) for C-algebras, Bull. London Math. Soc. 38 (2006), 857 - 867.
[2] B. Bekka, P. de la Harpe and A. Valette, Kazhdan’s Property (T), New Mathematical Monographs 11, Cambridge
University Press, Cambridge 2008.
[3] A. Connes and V. Jones, Property (T) for von Neumann algebras, Bull. London Math. Soc. 17 (1985), 51 - 62.
[4] Chi-Wai Leung and Chi-Keung Ng, Property (T) and strong Property (T) for unital C-algebras, J. Func. Anal.
256 (2009), 3055 - 3070.
[5] K. R. Davidson, C-algebras by example, Fields Inst. Monograph 6, Amer. Math. Soc., Providence 1996.
[6] P. Jolissaint, Property (T) for pairs of topological groups, Enseign. Math., 215 (2005), 31 - 45.
[7] D. Kazhdan, Connection of the dual space of a group with the structure of its closed subgroups, Funct. Anal.
Appl. (1967), 63 - 65.
[8] G. J. Murphy, C-algebras and operator theory, Academic Press, San Diego 1990.
[9] M. Takesaki, Theory of operator algebras, Springer, Berlin 2003.
[10] D. Williams, Crossed products of C-algebras, Math. Surveys Monogr., 134, Amer. Math. Soc., Providence