The Perturbation Of Weyl's Theorem For Upper Triangular Operator Matrices

In recent decades, the study of operator spectrum theory has been a popular branch of operator theory. Operator spectrum theory which not only takes a direct effect on modern mathematics, computational mathematics and nonlinear science, but also has major applications in quantum mechanics, modern physics, modern science and technology. In addition, perturbation theory of linear operator is closely linked with the disciplines of physics, engineering, quantum mechanics. Therefore, especially the perturbation of Weyl type theorem related to the distribution of eigen-value in quantum mechanics has been a significant subject in operator theory.In addition, with the development of linear operator theory, the study of op-erator matrices have increasingly brought people's attention, and have made cer-tain theoretical results. Let H is a complex separable Hilbert space, A ? B(H), B ? B(K), on the basis of existing theory, this paper mainly discussed the sta-bility of Weyl's theorem for upper triangular operator matrix that on H (?) K under compact perturbation and small compact perturbation, here, C ? B(K, H). In this paper, according to the spectral characteristics of A and B of upper triangular operator matrices Mc on the diagonal. we investigate the stability of upper triangular operator matrices and the square of upper triangular operator matrices of the Weyl's theorem under compact perturbation.This paper contains three chapters, more details is as follows:In Chapter 1, First, we introduce the related background and the basic symbol. Secondly, we also give the definition of the Weyl's theorem and Browder's theorem and so on.In Chapter 2, we investigate the stability of the Weyl's theorem and Browder's theorem under compact perturbation for the upper triangular operator matrices, and give the efficient and necessary conditions of upper triangular operator matrices satisfying the compact perturbation of Weyl's theorem, at the same time, we also to illustrate the essence of conditions in the theorem.In Chapter 3, we investigate the stability of the Weyl's theorem under compact perturbation for the square of upper triangular operator matrices, and give the effi-cient and necessary conditions for the square of upper triangular operator matrices satisfying the compact perturbation of Weyl's theorem, at the same time, we also to illustrate the essence of conditions in the theorem.