The Perturbation Relationship Between The Single-valued Extension Property And The Weyl Type Theorem

In the operator theory,the research of operator spectrum theory has always been an important issue which naturally draws much attention from both home and abroad.As many scholars research on spectral theory,they obtain lots of achieve-ments,and operator spectral theory is widely used in aspects such as modern science and technology,linear and nonlinear science,modern physics and computational mathematics.In the process of research of the spectrum theory,H.Weyl proposed Weyl’s theorem which was later generalized as Weyl’s type theorem by many schol-ars.Local spectral theory holds a central position in the spectral theory and the single valued extension property is indispensable in the research of local spectral theory.It facilitates people to better understand Weyl’s type theorem through the research of the single valued extension property.Therefore,many scholars carried out systematic studies on Weyl’s type theorem and gained many valuable conclu-sions.On the basis of these valuable documents,we further studies the relationship between the single valued extension property and Weyl’s type theorem under com-pact perturbations.In this paper,the specific arrangement is as follows:The first chapter describes the origin of the spectral theory,and the develop-ment and research status of Browder’s theorem and Weyl’s theorem.The definitions of relative spectral set as well as the definition and simple properties of Kato de-composition in a strictly generalized scope.The second chapter uses the new spectrum and discusses the relationship be-tween the single-valued extension property and Browder’s Theorem under small compact perturbations.At the same time,we discusses the relationship between the single valued extension property and the Weyl’s type theorem under small com-pact perturbations.The third chapter applies the new spectrum,we investigates the relation be-tween the single valued extension property and Weyl’s type theorem under the compact perturbation.In the end,we also characterizes the equivalence of the perturbation of Weyl’s type theorem and the single valued extension property.