三阶上三角算子矩阵点谱,连续谱和剩余谱的扰动

吴秀峰, 黄俊杰, 阿拉坦仓

数学学报 ›› 2015, Vol. 58 ›› Issue (3) : 423-430.

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数学学报 ›› 2015, Vol. 58 ›› Issue (3) : 423-430. DOI: 10.12386/A2015sxxb0042
论文

三阶上三角算子矩阵点谱,连续谱和剩余谱的扰动

    吴秀峰, 黄俊杰, 阿拉坦仓
作者信息 +

Perturbations of the Point Spectrum, Continuous Spectrum and Residual Spectrum for Third-Order Upper Triangular Operator Matrices

    Xiu Feng WU, Jun Jie HUANG, Alatancang
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文章历史 +

摘要

设 H1, H2,H3为无穷维复可分Hilbert空间, 记MD,E,F=∈B(H1⊕H2⊕H3). 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的点谱,连续谱和剩余谱随D, E, F扰动的完全描述.

Abstract

Let H1, H2, H3 be infinite-dimensional complex separable Hilbert spaces, and write MD,E,F = ∈ B(H1 ⊕ H2 ⊕ H3). Given the operators A ∈ B(H1), B ∈ B(H2), C ∈ B(H3), some complete descriptions of perturbations of the point spectrum, continuous spectrum and residual spectrum for the partial operator matrix MD,E,F are given, based on the analysis method and block operator technique.

关键词

算子矩阵 / 点谱 / 连续谱 / 剩余谱 / 扰动

Key words

operator matrix / point spectrum / continuous spectrum / residual spectrum / perturbation

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吴秀峰, 黄俊杰, 阿拉坦仓. 三阶上三角算子矩阵点谱,连续谱和剩余谱的扰动. 数学学报, 2015, 58(3): 423-430 https://doi.org/10.12386/A2015sxxb0042
Xiu Feng WU, Jun Jie HUANG, Alatancang. Perturbations of the Point Spectrum, Continuous Spectrum and Residual Spectrum for Third-Order Upper Triangular Operator Matrices. Acta Mathematica Sinica, Chinese Series, 2015, 58(3): 423-430 https://doi.org/10.12386/A2015sxxb0042

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基金

国家自然科学基金(11461049, 11371185); 内蒙古自治区自然科学基金(2013JQ01, 2013ZD01)

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