| 算子函数演算的广义Weyl定理 |
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| 引用本文： | 赵玲玲,曹小红.算子函数演算的广义Weyl定理[J].吉林大学学报(理学版),2017,55(5):1129-1134. |
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| 作者姓名： | 赵玲玲 曹小红 |
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| 作者单位： | 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 |
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| 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.
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| 关 键 词： | 广义Weyl定理 B-Weyl谱 Weyl定理 |
| 收稿时间： | 2016-10-19 |
Generalized Weyl’s Theorem for Functional Calculus of Operators |
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| ZHAO Lingling,CAO Xiaohong.Generalized Weyl’s Theorem for Functional Calculus of Operators[J].Journal of Jilin University: Sci Ed,2017,55(5):1129-1134. |
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| Authors: | ZHAO Lingling CAO Xiaohong |
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| Institution: | 1. Department of Fundamental Courses, Institute of Disaster Prevention, Sanhe 065201, Hebei Province, China;2. School of Mathematics and Information Science, Shaanxi Normal University, Xi’an 710119, China |
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| Abstract: | 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’stheorem. |
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| Keywords: | Weyl’s theorem generalized Weyl’s theorem B-Weyl’s spectrum |
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