Hilbert C ~ * - Model Shows The Theory Of The Relevant Issues

The theory of Hilbert C*modules has become very important in KK theory, C*algebraic quantum groups,classification of C*algebras and more,as well as being a fruitful a rea for the research of morden mathematics. The study of the theory of Hilbert C*modules becomes very important.For instance,the study of countably generated Hilbert C*-modules is significant in studying the structure of C*algebras and classification of C*algebras.In this paper, we mainly consider the theory of representations of Hilbert C*modules.Since the representations of Hilbert C*modules depend on the representations of the underlying C*-algebras,they have intimate relations between each other.similar to the representation theory of C*algebras, we have studied the representation theory of Hilbert C*modules.In the first chapter of this paper,basic concepts of Hilbert C*modules are given;in the second chapter,we present the necessary and sufficient cond itions for unitarily equivalence of cyclic representations in Hilbert C*modules; In the third chapter,we have studied some properties of induced represe ntations of quotient Hilbert C*modules and the properties of morp hisms between them; In the forth chapter, the definition of the primitive ideal submodules in Hilbert C*modules has been given.Some properties of primitive ideal submodule space and the spectrum space in Hilbert C*modules are studied.