华东师范大学学报（自然科学版） >

2016 , Vol. 2016 >Issue 6: 111 - 118

DOI: https://doi.org/10.3969/j.issn.1000-5641.2016.06.012

数学

微小摄动下SVEP与Weyl型定理的关系

  • 董 炯 ,
  • 曹小红 ,
  • 刘俊慧
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  • 陕西师范大学 数学与信息科学学院, 西安 710119

收稿日期: 2015-12-21

  网络出版日期: 2017-01-13

基金资助

国家自然科学基金(11371012, 11471200, 11571213); 陕西师范大学中央高校基本科研业务费专项资金(GK201601004, 2016CSY020)

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The relationship between SVEP and Weyl type theorem under small perturbations

  • DONG Jiong ,
  • CAO Xiao-hong ,
  • LIU Jun-hui
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  • School of Mathematics and Information Science, Shaanxi Normal University, Xi’an 710119, China

Received date: 2015-12-21

  Online published: 2017-01-13

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摘要

设H为复的无限维可分Hilbert空间, B(H)为H上有界线性算子的全体. 若σ(T)\σω(T)=π00(T), 则称T ∈ B(H)满足Weyl定理, 其中σ(T)和σω(T)分别表示算子T的谱和Weyl谱,π00(T)={λ ∈ isoσ(T): 0<dim N(T-λI)<∞}; 当σ(T)\σω(T)   π00(T), 时, 称T ∈ B(H)满足Browder定理. 本文利用算子的广义Kato分解性质, 刻画了算子在微小紧摄动下单值延拓性质(SVEP)与Weyl型定理之间的关系.

关键词： 单值延拓性质; Browder定理; Weyl定理

本文引用格式

董 炯 , 曹小红 , 刘俊慧 . 微小摄动下SVEP与Weyl型定理的关系[J]. 华东师范大学学报（自然科学版）, 2016 , 2016(6) : 111 -118 . DOI: 10.3969/j.issn.1000-5641.2016.06.012

Abstract

Let H be an infinite dimensional separable complex Hilbert space and B(H) be the algebra of all bounded linear operators on H. T ∈ B(H) satisfies Weyl’s theorem if σ(T)\σω(T)=π00(T),  where σ(T) and σω(T) denote the spectrum and the Weyl spectrum of T respectively, π00(T)={λ ∈ isoσ(T): 0<dim N(T-λI)<∞}. If σ(T)\σω(T)   π00(T),  T is called satisfying Browder’s theorem. In this paper, using the property of generalized Kato decomposition, we explore the relation between the single-valued extension property and Weyl’s theorem under small compact perturbations.

参考文献

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