K₀-Group And Approximate Similarity Invariants Of Strongly Irreducible Operator

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 T∈L(H) with connected spectrum andε＞0, there exists a strongly irreducible operator A, such that‖A-T‖＜ε, V(A'(A))≌N, K₀(A'(A))≌Z, and A'(A)/rad A'(A) is commutative, where A'(A) denotes the commutant of A and rad(A'(A)) denotes the Jacobson radical of A'(A).This paper includes four chapters. In chapter 1, we introduce the relative background in this paper and give some skeleton expressions of the original work. In chapter 2, we construct some kinds of strongly irreducible operators by operator theory and the technique of Banach algebra. In chapter 3, by some results of chapter 2, we characterize the unique strongly irreducible decomposition up to similarity of finitely direct sum of this operator. And by theory of approximation of operators, similarity orbit theorem and K theory, we get the main result of this paper. In chapter 4, we conclude the prime conclusion of this paper.