The Judgment Of Weyl's Theorem Of Operator And Its Perturbation

As a.significant branch of functional analysis,operator theory is payed attentions to by many scholars.And as a significant part of operator theory,the operator spectrym theory has naturally received much attention of many scholars.In recent decades,as domestic and foreign scholars research on spectral theory,they obtain lots of achievements.It not only has major applications in nonlinear science,modern mathematics and computational mathematics,but also plays an important role in quantum mechanics,modern physics.In the process of research of the spectrum theory,H.weyl proposed Weyl' s theorem which was later generalized as VVeyl's type theorem.This paper mainly defines a new spectral set for studying Weyl's theorem for operator functions and the compact perturbation of Weyl's theorem for linear operators.In addition,this paper also researches the perturbation of Weyl's theoremfor upper triangular operator matrix Mc ?(AC OB)?B(H(?)K)where A ?B(H),B? B(K),C ? B(K,H).In this paper,more details is as follows:In Chapter 1,we mainly introduce the related background and the basic sym-bol.we also give the definition of the related spectral set and the definition of Brow-der's theorem and Weyl's theorem and so on.In Chapter 2,we investigate the stability of the Weyl's theorem for bounded linear operators and the Weyl's theorem for operator functions under the new spectral set,and give their efficient and necessary conditions.In Chapter 3,we research the compact,perturbation of the Browder' s theorem and Weyl's theorem for upper triangular operator matrices under the new spectral set,and give their efficient and necessary conditions.