算子函数演算的广义Weyl定理  

Generalized Weyl's Theorem for Functional Calculus of Operators

作　　者：赵玲玲 曹小红[2] ZHAO Lingling CAO Xiaohong(Department of Fundamental Courses, Institute of Disaster Prevention, Sanhe 065201, Hebei Province, China School of Mathematics and Information Science, Shaanxi Normal University, Xi ＇an 710119, China)

机构地区：[1]防灾科技学院基础课教学部,河北三河065201 [2]陕西师范大学数学与信息科学学院,西安710119

出　　处：《吉林大学学报（理学版）》2017年第5期1129-1134,共6页Journal of Jilin University:Science Edition

基　　金：中国地震局教师科研基金(批准号:20150111);国家自然科学基金(批准号:11371012;11471200;11571213);陕西师范大学中央高校基本科研业务费专项基金(批准号:GK201601004);防灾科技学院教改项目(批准号:JY2017B09)

摘　　要：考虑Weyl定理的一种变型——广义Weyl定理,通过定义一种新谱集,利用该谱集给出算子T及其函数演算满足广义Weyl定理的充要条件,得到了算子T及其函数满足广义Weyl定理的新判别方法.We considered a variant of the Weyl＇s theorem：the generalized Weyl＇s theorem.By defining a new spectral set,we gave sufficient and necessary conditions for the operator T and its functional calculus to satisfy the generalized Weyl＇s theorem by using the spectral set.We obtained a new discriminant for T and its functional calculus to satisfy the generalized Weyl＇s theorem.

关 键 词：WEYL定理 广义Weyl定理 B-Weyl谱 

分 类 号：O177.2[理学—数学]