微小摄动下SVEP与Weyl型定理的关系

doi:10.3969/j.issn.1000-5641.2016.06.012

华东师范大学学报(自然科学版)

微小摄动下SVEP与Weyl型定理的关系

董炯, 曹小红, 刘俊慧

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 出版日期:2016-11-25 发布日期:2017-01-13
通讯作者: 曹小红, 女, 教授, 博士生导师, 研究方向为算子理论. E-mail: xiaohongcao@snnu.edu.cn.
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)

The relationship between SVEP and Weyl type theorem under small perturbations

DONG Jiong, CAO Xiao-hong, LIU Jun-hui

School of Mathematics and Information Science, Shaanxi Normal University, Xi’an 710119, China

Received:2015-12-21 Online:2016-11-25 Published:2017-01-13

摘要/Abstract

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)\σ_ω(T)=π₀₀(T), 则称T ∈ B(H)满足Weyl定理, 其中σ(T)和σ_ω(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)\σ_ω(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

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)\σ_ω(T)=π₀₀(T), where σ(T) and σ_ω(T) denote the spectrum and the Weyl spectrum of T respectively, π₀₀(T)={λ ∈ isoσ(T): 0<dim N(T-λI)<∞}. If σ(T)\σ_ω(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.

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), doi: 10.3969/j.issn.1000-5641.2016.06.012.

DONG Jiong, CAO Xiao-hong, LIU Jun-hui. The relationship between SVEP and Weyl type theorem under small perturbations[J]. Journal of East China Normal University(Natural Sc, doi: 10.3969/j.issn.1000-5641.2016.06.012.

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[2]	戴磊, 曹小红. 单值延拓性质的摄动及其应用[J]. 华东师范大学学报(自然科学版), 2014, 2014(6): 17-24.
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微小摄动下SVEP与Weyl型定理的关系

The relationship between SVEP and Weyl type theorem under small perturbations

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