Approximation And Similarity Classification Of Stably Finitely Strongly Irreducible Decomposable Operators

Let H be a complex separable Hilbert space and L(H) denote the collection of bounded linear operators on H. In this paper, we show that: For any operatorA∈L(H), there exists a stably finitely decomposable operator A_∈, such that‖A-A_∈‖＜∈and A'(A_∈)/rad A'(A_∈) is commutant, where rad A'(A_∈) is the Jacobson radical of A'(A_∈). Moreover, we give a similarity classification of the stably finitely decomposable operators, which follows similarity classification of Cowen-Douglas operators by C.L.Jiang.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 result of this paper. In chapter 3, by the results of the chapter 2 we get the the main result of this paper and give a similarity classification of the stably finitely decomposable operators. In chapter 4, the main results are given in this paper.