有界线性算子及其函数演算的Weyl定理  

Weyl's theorem for bounded linear operators and its functional calculus

作　　者：闫慧凰 曹小红[2] YAN Huihuang;CAO Xiaohong(Department of Mathematics,Changzhi University,Changzhi 046011,China;School of Mathematics and Information Science,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信息科学学院,陕西西安710119

出　　处：《中山大学学报（自然科学版）》2020年第2期22-27,共6页Acta Scientiarum Naturalium Universitatis Sunyatseni

基　　金：国家自然科学基金(11471200);陕西师范大学中央高校基本科研业务费专项基金(GK201601004)。

摘　　要：令B(H)为无限复可分的Hilbert空间H上的有界线性算子全体。若T∈B(H),定义H(T)为在T的谱集σ(T)的某个邻域上解析但在σ(T)的任一分支上不为常数的函数全体。利用新定义的谱集,研究了算子T及f(T)(f∈H(T))的Weyl定理,并刻画了T和f(T)满足Weyl定理的等价条件。另外利用所得的结论,探索了p-hyponormal(或M-hyponormal)算子的Weyl定理。Let B(H)be the set of all bounded linear operators on an infinite dimensional separable complex Hilbert space H.If T∈B(H),the set of all functions f which are analytic on a neighbourhood ofσ(T)and are not constants on any component ofσ(T)is denoted by H(T).Using the new spectrum,Weyl's theorem for T∈B(H)and f(T)(f∈H(T))is studied,and the necessary and sufficient conditions for both T and f(T)satisfying Weyl's theorem are characterized.Moreover,Weyl's theorem for p-hyponormal(or M-hyponormal)operators are explored.

关 键 词：BROWDER定理 WEYL定理 谱 p-hyponormal算子 

分 类 号：O177.2[理学—数学]