Strongly Irreducible Decompostion And Similarity Classification Of 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 if T = ,where and is commutative, and for any positive integer n and minimal idem-potent P ∈ A'(Tⁿ), A'(Tⁿ|PHⁿ)/radA'(Tⁿ|PHⁿ) is commutative, then T is a stably finitely decomposable operator, and has a stably unique (SI) decomposition up to similarity. Moreover, we give a similarity classification of the operators which satisfy the conditions above by using the K₀-group of the commutant algebra as an invariant.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 characterize the stably unique strongly irreducible decomposition up to similarity of this operator by K₀ group. 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 operators which satisfy the conditions above. In chapter 4, the main results are given in this paper.