| 上三角算子矩阵的单值延拓性质的摄动 |
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| 引用本文： | 曹小红,吴学俪,张敏.上三角算子矩阵的单值延拓性质的摄动[J].数学学报,2016,59(4):451-460. |
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| 作者姓名： | 曹小红 吴学俪 张敏 |
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| 作者单位： | 陕西师范大学数学与信息科学学院 西安 710062 |
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| 基金项目： | 国家自然科学基金资助项目(11371012,11471200,11571213);陕西师范大学中央高校基本科研业务费专项资金资助项目(GK201601004) |
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| 摘 要： | 设H为无限维可分的复Hilbert空间,B(H)为H上的有界线性算子全体.算子T∈B(H)称为具有单值延拓性质,若对任意一个开集U(?)C,满足方程(T-λI)f(λ)=0(任给λ∈U)的唯一的解析函数f:U→H为零函数;T∈B(H)称为满足单值延拓性质的稳定性,若对任意一个紧算子K∈B(H),T+K都满足单值延拓性质.本文给出了2×2上三角算子矩阵在紧摄动下满足单值延拓性质的稳定性的特征.
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| 关 键 词： | 单值延拓性质 紧摄动 谱 |
The Perturbation of the Single Valued Extension Property for Upper Triangular Operator Matrices |
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| Xiao Hong CAO,Xue Li WU,Min ZHANG.The Perturbation of the Single Valued Extension Property for Upper Triangular Operator Matrices[J].Acta Mathematica Sinica,2016,59(4):451-460. |
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| Authors: | Xiao Hong CAO Xue Li WU Min ZHANG |
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| Institution: | College of Mathematics and Information Science, Shaanxi Normal University, Xi'an 710062, P. R. China |
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| Abstract: | Let H be an infinite-dimensional separable complex Hilbert space and B(H) be the algebra of all bounded linear operators on H. An operator T∈B(H) is said to have the single-valued extension property, if for every open set U?C, the only analytic solution f:U→H of the equation (T-λI)f(λ)=0 for all λ∈U is zero function on U; T∈B(H) is said to have the stability of the single-valued extension property if T+K has the single-valued extension property for any compact operator K∈B(H). In this paper, we characterize 2×2 upper triangular operator matrices for which the single valued extension property is stable under compact perturbations. |
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| Keywords: | single-valued extension property compact perturbations spectrum |
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