3×3阶上三角算子矩阵的点谱和剩余谱扰动

PERTURBATION OF THE POINT AND RESIDUAL SPECTRA OF 3×3 UPPER TRIANGULAR OPERATOR MATRICES

基于值域的稠密性和闭性,有界线性算子T的点谱和剩余谱可分别细分为σ_(p,1)(T),σ_(p,2)(T)和σ_(r,1)(T),σ_(r,2)(T).设H_1,H_2,H_3为无穷维复可分Hilbert空间,给定A∈B(H_1),B∈B(H_2),C∈B(H_3),结合分析方法与算子分块技巧给出了M_(D,E,F)的上述四种谱随D,E,F扰动的完全描述.

The point and residual spectra of a bounded operator T are,respectively,split into σ_（p,1）（T）,σ_（p,2）（T） and σ_（r,1）（T）,σ_（r,2）（T）,based on the denseness and closedness of its range.Let H_1,H_2,H_3 be infinite dimensional complex separable Hilbert spaces.Given the operators A ∈ B（H_1）,B ∈ B（H_2） and C ∈ B（H_3）,some complete characterizations on the perturbations of the previous four spectra for the partial operator matrix M_（D,E,F） are given by means of the analysis method and block operator technique.