a-Weyl定理的判定及其摄动

doi:10.6040/j.issn.1671-9352.0.2017.187

山东大学学报（理学版） ›› 2017, Vol. 52 ›› Issue (10): 77-83.doi: 10.6040/j.issn.1671-9352.0.2017.187

a-Weyl定理的判定及其摄动

孔莹莹¹,曹小红^1*,戴磊²

1.陕西师范大学数学与信息科学学院, 陕西西安 710119;2.渭南师范学院数理学院, 陕西渭南 714099

收稿日期:2017-04-26 出版日期:2017-10-20 发布日期:2017-10-12
通讯作者: 曹小红(1972— ), 女, 博士, 教授, 博士生导师, 研究方向为算子理论. E-mail:xiaohongcao@snnu.edu.cn E-mail:yingyingkongshida@163.com
作者简介:孔莹莹(1994— ), 女, 硕士研究生, 研究方向为算子理论. E-mail:yingyingkongshida@163.com
基金资助:
国家自然科学基金资助项目(11471200,11501419,11371012,11571213);陕西师范大学中央高校基本科研业务费专项资金资助(GK201601004);渭南市科技计划项目(2016KYJ-3-3);陕西省教育厅项目(17JK0279);渭南师范学院自然科学人才项目(15ZRRC10)

Judgement of a-Weyls theorem and its perturbations

KONG Ying-ying¹, CAO Xiao-hong^1*, DAI Lei²

1. School of Mathematics and Information Science, Shaanxi Normal University, Xian 710119, Shaanxi, China;
2. College of Mathematics and Physics, Weinan Normal University, Weinan 714099, Shaanxi, China

Received:2017-04-26 Online:2017-10-20 Published:2017-10-12

摘要/Abstract

摘要： 设H为无限维复可分的Hilbert空间, B(H)为H上的有界线性算子的全体。 T∈B(H)称为是满足a-Weyl定理, 若σa(T)\σ_aw(T)=πa₀₀(T), 其中σa(T), σ_aw(T)分别表示算子T∈B(H)的逼近点谱和本质逼近点谱, πa₀₀(T)={λ∈iso σa(T):0<dim N(T-λI)<∞}。本文通过定义新的谱集, 给出了算子演算满足a-Weyl定理的判定方法, 同时也考虑了a-Weyl定理的摄动。

关键词: a-Weyl定理, 逼近点谱, 紧摄动

Abstract: Let H be an infinite dimensional separable complex Hilbert space and B(H) the algebra of all bounded linear operators on H. For T∈B(H), we call a-Weyls theorem holds for T if σ_a(T)\σ_aw(T)=π^a₀₀(T), where σ_a(T)and σ_aw(T)denote the approximate point spectrum and essential approximate point spectrum respectively, and π^a₀₀ (T)={λ∈iso σ_a(T):0N(T-λI)<∞}. Using the new spectrum defined in this paper, we investigate a-Weyls theorem for operator functional. In addition, we explore the compact perturbation of a-Weyls theorem.

Key words: approximate point spectrum, a-Weyls theorem, compact perturbation

中图分类号:

O177.2

孔莹莹,曹小红,戴磊. a-Weyl定理的判定及其摄动[J]. 山东大学学报（理学版）, 2017, 52(10): 77-83.

KONG Ying-ying, CAO Xiao-hong, DAI Lei. Judgement of a-Weyls theorem and its perturbations[J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2017, 52(10): 77-83.

参考文献

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a-Weyl定理的判定及其摄动

Judgement of a-Weyls theorem and its perturbations

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