Study On The Weyl Type Theorems Of The Operators On The Banach Spaces

Recently,some famous mathematicians concentrate on the research on Weyl type theorems.It leads a series of researches on Weyl type theorem by many other researchers.Under this context,we discuss Weyl type theorems and extended prop-erties on Banach space.In chapter 1,the property(aw)and(gaw)are variants of Weyl type theorem,for a bounded linear operator T acting on a Banach space.We establish for T the necessary and sufficient conditions for which the property(aw)and(gaw)holds by means of SVEP.Also,we study the stability of property(aw)and(gaw)under perturbations by power finite rank operators commuting with T;In chapter 2,we study the single valued extension property and property(aw);In chapter 3,we study topological uniform descent and the single valued extension property.