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.