Weyl定理与(R)性质的判定  

The Judgment of Weyl's Theorem and Property(R)

作　　者：赵巨涛[1] 曹小红 董炯[1] ZHAO Jutao;CAO Xiaohong;DONG Jiong(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,长治046011 [2]陕西师范大学数学与统计学院,西安710119

出　　处：《华南师范大学学报（自然科学版）》2023年第2期109-115,共7页Journal of South China Normal University(Natural Science Edition)

基　　金：国家自然科学基金项目(12101081)。

摘　　要：利用半Fredholm算子的扰动不变性,研究有界线性算子与上三角算子矩阵的Weyl型定理。首先,给出有界线性算子同时满足Browder定理和(R_(1))性质,或者同时满足Weyl定理和(R)性质的充要条件;然后,讨论上三角算子矩阵同时满足Weyl定理和(R)性质的条件。The perturbation invariance of semi-Fredholm operators are used to study Weyl type theorems for boun-ded linear operators and upper triangular operator matrices.First,the necessary and sufficient conditions for which both the property(R_(1))and Browder's theorem hold or both the property(R)and Weyl's theorem hold for bounded linear operators are given.In addition,the conditions for which both the property(R)and Weyl's theorem hold for upper triangular operator matrices are explored.

关 键 词：有界线性算子 上三角算子矩阵 (R)性质 WEYL定理 谱 

分 类 号：O177.1[理学—数学]