上三角算子矩阵Weyl型定理的稳定性判定

殷俊强; 曹小红

doi:10.7523/j.issn.2095-6134.2013.05.003

中国科学院大学学报 >

2013 , Vol. 30 >Issue 5: 591 - 597

DOI: https://doi.org/10.7523/j.issn.2095-6134.2013.05.003

数学

上三角算子矩阵Weyl型定理的稳定性判定

殷俊强 ,
曹小红

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陕西师范大学数学与信息科学学院, 西安 710062

收稿日期: 2012-07-06

修回日期: 2012-10-31

网络出版日期: 2013-09-15

基金资助

陕西师范大学中央高校基本科研业务费专项资金(GK200901015)资助 

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Judgement on stability of Weyl’s theorem for the upper triangular operator matrices

YIN Jun-Qiang ,
CAO Xiao-Hong

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College of Mathematics and Information Science, Shaanxi Normal University, Xi'an 710062, China

Received date: 2012-07-06

Revised date: 2012-10-31

Online published: 2013-09-15

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摘要

称算子T满足a-Browder定理,若σ_a(T)\σ_ea(T)???π₀₀^a(T),其中σ_a(T)和σ_ea(T)分别表示算子T的逼近点谱和本质逼近点谱,和π₀₀^a(T)={λ∈isoσ_a(T),0< dimN(T-λI)<∞}. 若σ_a(T)\σ_ea(T)=π₀₀^a(T), 则称算子T 满足a-Weyl定理. 利用上三角算子矩阵中主对角线上的算子的半Fredholm域的特征, 研究上三角算子矩阵a-Browder定理和a-Weyl定理在紧摄动下的稳定性.

关键词： 上三角算子矩阵; a-Browder定理; 紧摄动; 渐近纠缠算子; 半Fredholm域

本文引用格式

殷俊强 , 曹小红 . 上三角算子矩阵Weyl型定理的稳定性判定[J]. 中国科学院大学学报, 2013 , 30(5) : 591 -597 . DOI: 10.7523/j.issn.2095-6134.2013.05.003

Abstract

An operator T is said to satisfy a-Browder's theorem if σ_a(T)\σ_ea(T)???π₀₀^a(T), where σ_a(T) and σ_ea(T) denote the approximate point spectrum and the essential approximate point spectrum, respectively, and π₀₀^a(T)={λ∈isoσ_a(T),0< dimN(T-λI)<∞}. If σ_a(T)\σ_ea(T)=π₀₀^a(T), we say that T satisfies a-Weyl's theorem. In this note, by using the characteristics of semi-Fredholm domain of the diagonal of the upper triangular operator matrix, we investigate the stability of a-Browder's theorem and a-Weyl's theorem for the upper triangular operator matrices under compact perturbations.

Key words： upper triangular operator matrices; a-Browder’s theorem; compact perturbations; asymptotic intertwining operator; semi-Fredholm domain

参考文献

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