2 × 2-上三角算子矩阵谱的Fredholm扰动

张世芳, 钟怀杰, 武俊德

数学学报 ›› 2011, Vol. 54 ›› Issue (4) : 581-590.

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PDF(371 KB)
数学学报 ›› 2011, Vol. 54 ›› Issue (4) : 581-590. DOI: 10.12386/A2011sxxb0059
论文

2 × 2-上三角算子矩阵谱的Fredholm扰动

    张世芳1,2, 钟怀杰2, 武俊德1
作者信息 +

Fredholm Perturbation of Spectra of 2 × 2-Upper Triangular Matrices

    Shi Fang ZHANG1,2, Huai Jie ZHONG2, Jun De WU1
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文章历史 +

摘要

HK是复无穷维可分Hilbert空间, AB(H), BB(K), CB(K, H)且MC=(0ABC). 本文给出了上三角算子矩阵MC的 Weyl 谱、本性谱、谱、左谱、右谱、下半本性谱、下半 Weyl谱 和上半Weyl谱的Fredholm 扰动的完全刻画.  

Abstract

Let H and K be complex infinite dimensional separable Hilbert spaces, AB(H), BB(K), CB(K,H) and MC = (0ABC). In this paper, we characterize completely the Fredholm perturbation for the Weyl spectrum, essential spectrum, spectrum, left spectrum, right spectrum, lower semi-Fredholm spectrum, lower semi-Weyl spectrum and upper semi-Weyl spectrum of the upper triangular operator matrices MC.  

关键词

Banach空间 / 上三角算子矩阵 / / 扰动

Key words

Banach spaces / upper-triangular operator matrices / spectra / perturbation

引用本文

导出引用
张世芳, 钟怀杰, 武俊德. 2 × 2-上三角算子矩阵谱的Fredholm扰动. 数学学报, 2011, 54(4): 581-590 https://doi.org/10.12386/A2011sxxb0059
Shi Fang ZHANG, Huai Jie ZHONG, Jun De WU. Fredholm Perturbation of Spectra of 2 × 2-Upper Triangular Matrices. Acta Mathematica Sinica, Chinese Series, 2011, 54(4): 581-590 https://doi.org/10.12386/A2011sxxb0059

参考文献

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基金

国家自然科学基金(10771034, 10771191,10471124);福建省自然科学基金(Z0511019, S0650009)

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