微小摄动下SVEP与Weyl型定理的关系

董炯; 曹小红; 刘俊慧

doi:10.3969/j.issn.1000-5641.2016.06.012

微小摄动下SVEP与Weyl型定理的关系

doi: 10.3969/j.issn.1000-5641.2016.06.012

1.
陕西师范大学数学与信息科学学院, 西安 710119

基金项目:

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)

详细信息

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.

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出版历程
- 收稿日期: 2015-12-21
- 刊出日期: 2016-11-25

The relationship between SVEP and Weyl type theorem under small perturbations

1.
School of Mathematics and Information Science, Shaanxi Normal University, Xi’an 710119, China

摘要

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(T)\(T)=00(T), 则称T B(H)满足Weyl定理, 其中(T)和(T)分别表示算子T的谱和Weyl谱,00(T)={ iso(T): 0dim N(T-I)}; 当(T)\(T) 00(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.
- 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 Weyls theorem if(T)\(T)=00(T), where (T) and(T) denote the spectrum and the Weyl spectrum of T respectively,00(T)={ iso(T): 0dim N(T-I)}. If(T)\(T) 00(T), T is called satisfying Browders theorem. In this paper, using the property of generalized Kato decomposition, we explore the relation between the single-valued extension property and Weyls theorem under small compact perturbations.

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参考文献(1)

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