Study On The Weyl Type Theorems For The Bounded Linear Operators

Recently, many scholars research the Weyl type theorems from various aspects, and constantly enrich the Weyl type theorems. We further discuss the Weyl type theorems of the bounded linear operators on the Banach space. This paper consists four chapters. In chapter1, we introduce and study the new spectral properties (Q),(QQ),(qaW) and(qaB), which are related to the Weyl type theorems. Then we discuss the relation between the new spectral properties and other Weyl type theorems. We also study the perturbations and direct sum results of them. In chapter2, we first study the relation between the properties (z) and (az) of the operators, then we discuss the relation between the properties (z) and (az) of the operator matrices MO and MC.we also discuss the Browder spectrum for upper triangular block operator of order n. In chapter3, we study the relation between the Weyl type theorems for the operator T and restriction of operator Tn. In chapter4, we discuss the Weyl type theorems for algebraically k-quasi-class A operators.