Research On The (?₁) And (?) Properties Of Operators

The operator spectral theory,a favorite branch of functional analysis,has been widely concerned and studied by scholars at home and abroad in recent decades.In the new century,the operator spectral theory,achieving fruitful results,has been promoted by many scholars.These achievements not only play an extremely impor-tant role in mathematics,but also play an important role in quantum mechanics.In 1990,in the process of studying operator spectral theory,H.Weyl defined Weyl the-orem.Then,scholars transformed and generalized Weyl theorem,Rakocevic defined property(?1)and property(?)of the bounded linear operators.In this paper,on the basis of existing theories,we study property(?1)and property(?)of bounded linear operators by defining new spectral sets.Meanwhile,we also study property(?)of hypercyclic operators.The full text is divided into three chapters,the specific contents are as follows:In Chapter 1,we introduce the related background and fundamental symbols,we also give the definitions of property(?1),property(?)and the new spectrum.In Chapter 2,we use the new spectrum that is defined by using the single-valued extension property to discuss the determination methods of property(?1)of bounded linear operators.In Chapter 3,using the new spectrum that is defined by single-valued extension property,we investigate the determination methods of property(?)of bounded linear operators and property(?)of hypercyclic operators.