Consistent Fredholm Index Operator And Weyl's Theorem Research

Spectral theory is an important branch of operator theory in operator algebra,it is closely related to other disciplines,it is widely used in physics,quantum mechanics and other disciplines.The Weyl type theorem in spectral theory has attracted much attention in recent years,the research on the problem and related problems has become a hot topic in spectrum theory.This thesis uses the property of consistency in Fredholm index,researching the methods for operator which Weyl's theorem,Browder's theorem,a-Weyl's theorem and a-Browder's theorem holds,and researching the relations of these theorems.This thesis contains four chapters,the following is more details:In chapter 1,we introduce the research's background and current situation,we also give the definition of Weyl's theorem,a-Weyl's theorem,Browder's theorem,aBrowder's theorem and consistent Fredholm index operators.Based on the property of consistency in Fredholm index,we give a new spectrum ?1(T).In chapter 2,using the new spectrum defined before,we give the judgments for T and T*which Browder's theorem and Weyl's theorem hold.In chapter 3,using the new spectrum defined before,we give the judgments for T and T*which a-Browder's theorem and a-Weyl's theorem hold.In chapter 4,We give the necessary and sufficient conditions for the operator T and T*to satisfy both a-Browder's theorem and a-Weyl's theorem are given.