有界线性算子的一致Fredholm指标性质及Weyl型定理  

The property of consistent Fredholm index and Weyl type theorems for bounded linear operators

作　　者：赵巨涛[1] 曹小红 Zhao Jutao;Cao Xiaohong(Department of Mathematics,Changzhi University,Changzhi 046011,China;School of Mathematics and Statistics,Shaanxi Normal University,Xi'an 710119,China)

机构地区：[1]长治学院数学系,山西长治046011 [2]陕西师范大学数学与统计学院,西安710119

出　　处：《河南师范大学学报（自然科学版）》2022年第5期42-48,共7页Journal of Henan Normal University(Natural Science Edition)

基　　金：国家自然科学基金(12101081);陕西省自然科学基金(2021JM-519);山西省基础研究计划资助项目(20210302124079).

摘　　要：Weyl型定理反映了线性算子的局部谱结构,对Weyl型定理的研究是算子谱理论研究的热点问题,近年来备受关注.利用一致Fredholm指标性质,给出了有界线性算子或算子函数同时满足(R)性质和Weyl定理的充要条件.之后有界线性算子或者算子函数的(R)性质、Weyl定理及亚循环性三者之间的关系得到了讨论.Weyl type theorem reflects the local spectral structure of linear operators.The study of Weyl type theorem is a hot issue in the study of operator spectrum theory,which has attracted much attention in recent years.In this paper,using the consistent Fredholm index property,we give the sufficient and necessary conditions for both Weyl’s theorem and property(R)hold.In addition,the relations among the property(R),Weyl’s theorem and the hypercyclic property for a bounded linear operator or its functional are taken into consideration.

关 键 词：(R)性质 BROWDER定理 WEYL定理 亚循环性 谱 

分 类 号：O177.2[理学—数学]