A Study On The Spectral Properties And Others On Banach Spaces

Recently,many scholars concentrate on the research on spectral properties and so that the spectral theory of operator has been greatly enriched.Under this context,we further discuss spectral properties of bounded linear operators on Banach spaces.This paper composed by four contents.In chapter 1,we introduce the prerequisites,it includes some theorems and definitions which have existed.In chapter 2,we study the new spectral properties(J),(gJ),(BgJ)and(BgR).Then we discuss the relation between the new spectral properties and other Weyl type theorems.We also study the perturbations of them.In chapter 3,we study these new spectral properties for direct sums.In chapter 4,we study the spectral properties of operator matrices and other related contents.