| 摘要: |
| 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σp,1(T),σp,2(T)和σr,1(T),σr,2(T).设H1,H2,H3为无穷维复可分Hilbert空间,给定A∈B(H1),B∈B(H2),C∈B(H3),结合分析方法与算子分块技巧给出了MD,E,F的上述四种谱随D,E,F扰动的完全描述. |
| 关键词: 算子矩阵 点谱 剩余谱 扰动 |
| DOI： |
| 分类号:O177.1;O177.7 |
| 基金项目:国家自然科学基金资助(11461049;11371185);内蒙古自治区自然科学基金资助(2013JQ01). |
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| PERTURBATION OF THE POINT AND RESIDUAL SPECTRA OF 3×3 UPPER TRIANGULAR OPERATOR MATRICES |
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HUANG Jun-jie, WU Xiu-feng, Alatancang
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School of Mathematical Sciences, Inner Mongolia University, Hohhot 010021, China
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| Abstract: |
| The point and residual spectra of a bounded operator T are, respectively, split into σp,1(T), σp,2(T) and σr,1(T), σr,2(T), based on the denseness and closedness of its range. Let H1, H2, H3 be infinite dimensional complex separable Hilbert spaces. Given the operators A∈B(H1), B∈B(H2) and C∈B(H3), some complete characterizations on the perturbations of the previous four spectra for the partial operator matrix MD,E,F are given by means of the analysis method and block operator technique. |
| Key words: operator matrix point spectrum residual spectrum perturbation |
