Property(T)of C~*-algebras

In this dissertation, we mainly study property (T) of C*-algebras and its invariance under the exact extension. In Chapter1, we introduce the background and basic definitions of this dissertation. In Chapter2, we give an equivalent theorem of property (T), which simplifies the definition of property (T) by the cyclic Hilbert bimodule, and prove that property (T) is invariant under C*-algebraic extension. In Chapter3, we show that strong property (T) is invariant under the extension of C*-algebras. We also show that the strong property (T) is invariant under the action by tensor product and crossed product, and the induced C*-algebras with property (T) still invariant under the exact extension.