Determination Of (?) Properties Of Bounded Linear Operators

The operator Spectral theory is an important branch of operator theory and operator algebra in operator theory.It is closely related to other disciplines and has attracted much attention in recent years.In the new century,with the promotion of more scholars,the theory of operator spectrum has achieved remarkable results.These achievements play a very important role not only in mathematics,but also in the field of quantum information.In 1909,H.Weyl proposed the Weyl theorem in the research process of operator spectrum theory,and later scholars deformed and extended the Weyl theorem.Rakocevic V gave another deformed(?1)and(?)property of Weyl theorem.Based on the existing theory,this paper studies the properties of(?1)and(?)property by using the new spectral set defined by Kato property.This paper consists of three chapters.In Chapter 1,this paper expounds the research background,research status,preliminary knowledge and some related symbols,and gives the definition of(?1)property,(?)property and related spectrum set.In Chapter 2,based on the spectrum set defined by Kato property,the paper explores the boundary operators and the determination method of operator function satisfying the property of(?1).In Chapter 3,using the new spectrum set defined by Chapter 2,the paper explores the boundary operators and the determination method of operator function satisfying the property of(?).