Study On Weyl Type Theorem

Recently, some famous mathematicians concentrate on the research on Weyl type theorems. It leads a series of researches on Weyl type theorems by many other researchers. Under this context, we systematically study the Weyl type theorems and their affiliated content. In chapter1, based on the structure of the spectrum of linear operator on Banach space, we describe the two kinds of structures of the approximate spectrum and surjective spectrum. In chapter2, we define certain kinds of new properties which extended the Weyl type theorems. Then, we discuss the relationship between the new properties and Weyl type theorems. And, also, we study the perturbations results and direct sum results of them. In chapter3, we consider the Weyl type theorems under topological uniform descent. Meanwhile, we utilise the Topological uniform descent to give the equivalent characterization of Weyl type theorems. In chapter4, new properties of Weyl type theorems are extended to operator matrices.