Weyl型定理与单值延拓性质的等价性

吉林大学学报(理学版)

Weyl型定理与单值延拓性质的等价性

刘俊慧, 曹小红, 董炯

陕西师范大学数学与信息科学学院, 西安 710119

收稿日期:2015-12-03 出版日期:2016-09-26 发布日期:2016-09-19
通讯作者: 曹小红 E-mail:xiaohongcao@snnu.edu.cn

Equivalence between Weyl Type Theorem andSingle Valued Extention Property

LIU Junhui, CAO Xiaohong, DONG Jiong

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

Received:2015-12-03 Online:2016-09-26 Published:2016-09-19
Contact: CAO Xiaohong E-mail:xiaohongcao@snnu.edu.cn

摘要/Abstract

摘要：

利用算子的严格广义Kato分解性质, 研究算子的单值延拓性质与Weyl型定理在紧摄动下的稳定性以及Weyl型定理与单值延拓性质紧摄动之间的关系, 得到了Weyl型定理摄动与单值延拓性质摄动等价的充要条件.

关键词: 严格广义Kato分解, 单值延拓性质, Weyl型定理

Abstract:

Using the strictly generalized Kato decomposition property of operator, we investigated the stability of the single valued extension property of the operator and the Weyl type theorem under compact perturbations. In addition, we also discussed the relation between the Weyl type theorem and the single valued extension property under compact perturbation. Then we obtained the sufficient and necessary conditions for the equivalence of the perturbation of Weyl type theorem and single valued extension property.

Key words: strictly generalized Kato decomposition, single valued extension property, Weyl type theorem

中图分类号:

O177.2

刘俊慧, 曹小红, 董炯. Weyl型定理与单值延拓性质的等价性[J]. 吉林大学学报(理学版), 2016, 54(05): 969-976.

LIU Junhui, CAO Xiaohong, DONG Jiong. Equivalence between Weyl Type Theorem andSingle Valued Extention Property[J]. Journal of Jilin University Science Edition, 2016, 54(05): 969-976.