算子函数演算的a-Weyl定理的判定  

A-Weyl’s theorem for functional calculus of operator

作　　者：孙晨辉 曹小红 SUN Chenhui;CAO Xiaohong(School of Mathematics and Statistics,Weinan Normal University,Weinan 714099,Shaanxi,China;School of Mathematics and Statistics,Shaanxi Normal University,Xi’an 710062,Shaanxi,China)

机构地区：[1]渭南师范学院数学与统计学院,陕西渭南714099 [2]陕西师范大学数学与统计学院,陕西西安710062

出　　处：《云南大学学报（自然科学版）》2024年第6期1001-1008,共8页Journal of Yunnan University(Natural Sciences Edition)

基　　金：陕西省教育厅专项科研计划(21JK0637);陕西省教育科学“十三五”规划青年课题(SGH20Q254);渭南师范学院2021年人才项目(2021RC16);2022年度渭南市科技局科技计划(2022ZDYFJH-11).

摘　　要：运用新定义的谱集,给出了判定有界线性算子满足a-Weyl定理的新方法.进一步通过该谱集,刻画了算子函数演算满足a-Weyl定理及(ω)性质的充要条件,并讨论了亚循环算子与其函数演算满足a-Weyl定理的关系.By using the newly defined spectrum set,the new judgement of a-Weyl’s theorem for bounded linear operators is given.In addition,the necessary and sufficient conditions for operator functions satisfying a-(ω)Weyl’s theorem and property are characterized.Moreover,the relation between hypercyclic operators and a-Weyl’s theorem for its functional calculus is discussed.

关 键 词：a-Weyl定理 算子函数演算 谱 

分 类 号：O177.2[理学—数学]