Study Weyl Type Theorem Of Operator On Banach Space

Recently,more and more scholars research the Weyl type theerems from many different angles,and a series of fruitful results have been achieved based on back-ground,our dissertation explores the Weyl type theorems of the bounded linear operator on the Banach space.This paper is divided into four chapter.In chapter 1,we introduce four kinds of new properties which extended the Weyl type the-orems.Then,we discuss the relationship between new properties and Weyl type theorems.And,also,we study their perturbations results.In chapter 2,we con-tinue to study their direct sum results,and the properties for Tn,the restriction of operator T.In chapter 3,we consider mainly properties which were called(gy)and(gby)of Weyl type theorems on the operator matrices.In chapter 4,we study properties of quasi-K-para.normal operators.Moreover,we discuss the Weyl type theorems for algebraically quasi-K-paranormal operators and completely algebraic quasi-K-paranormal operators.