Spectral Representation Theorem Of Cowen-Douglas Operators

Let H be a complex separable Hilbert space and L(H) denote the collection of bounded linear operators on H. In this paper, by the tools of Banach algebra and complex geometry, we study the properties of Cowen-Douglas operators and their commutants, and then by the Gelfand theory and strongly irreducible decomposition of operators, give the spectral representation theorem of these operators.This paper contains four chapters. In chapter 1, we introduce the relative background on this paper and give some skeleton expressions of the original work. In chapter 2, we introduce the preliminary results about Banach algebra and complex geometry.In chapter 3, by the results of the chapter 2, we study the the commutant of Cowen-Douglas operators and then establish the spectral representation theorem of Cowen-Douglas operators. In chapter 4, the main results are given in this paper.