1Department of Mathematics, Azarbaijan Shahid Madani University, Tabriz, Islamic Republic of Iran.
2Faculty 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).
 M. B. Bekka, Property (T) for C∗-algebras, Bull. London Math. Soc. 38 (2006), 857 - 867.  B. Bekka, P. de la Harpe and A. Valette, Kazhdan’s Property (T), New Mathematical Monographs 11, Cambridge University Press, Cambridge 2008.  A. Connes and V. Jones, Property (T) for von Neumann algebras, Bull. London Math. Soc. 17 (1985), 51 - 62.  Chi-Wai Leung and Chi-Keung Ng, Property (T) and strong Property (T) for unital C∗-algebras, J. Func. Anal. 256 (2009), 3055 - 3070.  K. R. Davidson, C∗-algebras by example, Fields Inst. Monograph 6, Amer. Math. Soc., Providence 1996.  P. Jolissaint, Property (T) for pairs of topological groups, Enseign. Math., 215 (2005), 31 - 45.  D. Kazhdan, Connection of the dual space of a group with the structure of its closed subgroups, Funct. Anal. Appl. (1967), 63 - 65.  G. J. Murphy, C∗-algebras and operator theory, Academic Press, San Diego 1990.  M. Takesaki, Theory of operator algebras, Springer, Berlin 2003.  D. Williams, Crossed products of C∗-algebras, Math. Surveys Monogr., 134, Amer. Math. Soc., Providence 2007.