The Stability Of The Single Valued Extension Prorerty For The Asymptotic Intertwining Operators

The spectral of normal operators enables people to obtain a deep understanding of the internal structure of normal operators, one of the most fundamental objects in operator theory is to find meaningful generalizations of the theory of normal operators. There is no doubt that the local theory is one of the most satisfactory generalizations, throughout the study the local spectra theory, the single valued extension property always plays a key role. Perturbation theory of linear operator is closely linked with the disciplines of physics, engineering, quantum mechanics, especially the perturbation of Weyl type theorems related to the distribution of eigenvalue in quantum mechanics, has been an impressive key branch in operator theory.The main content of the paper is the stability of the single valued extension property for the asymptotic intertwining operators and the upper triangular operator matrices, also, we study the stability of Weyl type theorem for the upper triangular operator matrices.This paper contains three chapters:In chapter1, given the historical background of this study, prepare knowledge and the definition of the asymptotic intertwining operators and some properties of the spectrum.In chapter2, through the various spectral sets, we investigate the stability of the single valued extension property for the asymptotic intertwining operators. At the same time, we use all kinds of spectral sets of operators on the main diagonal to investigate the stability of the single valued extension property for the upper triangular operator matrices.In chapter3, the first, we study the equivalent condition of a single operator to satisfy a-Browder’s theorem. The second, using the characteristics of semi-Fredholm domain of the diagonal of the operator matrix, we investigate the stability of the upper triangular operator matrices of the a-Browder’s theorem and a-Weyl’s theorem under compact perturbations.