摘要
设H为无限维复可分的Hilbert空间,B(H)为H上的有界线性算子的全体,T∈B(H)称为满足(R)性质,若σ_(a)\σ_(ab)(T)=π∞(T),其中σ_(a)(T)和σ_(ab)(T)分别表示算子T的逼近点谱和Browder本质逼近点谱,π∞(T)={λ∈isoσ(T):0<dimN(T-λΙ)<∞|.利用拓扑一致降标性质,首先给出了有界线性算子满足(R)性质的充要条件;之后通过拓扑一致降标性质,得到了算子函数满足(R)性质的判定方法;最后,上三角算子矩阵的(R)性质得到了研究。
Let H be a complex separable infinite dimensional Hilbert space and B(H)be the algebra of all bounded linear operators on H,T∈B(H)is said to satisfy property(R)ifσ_(a)\σ_(ab)(T)=π∞(T),whereσ_(a)(T)andσ_(ab)(T)denote the approximate point spectrum and the Browder essential approximate point spectrum of T respectively,andπ∞(T)={λ∈isoσ(T):0<dimN(T-λΙ)<∞|.By using the property of topological uniform descent,the necessary and sufficient conditions for which the property(R)holds for bounded linear operators are given.In addition,the new judgements for operator functions satisfying property(R)according to the property of topological uniform descent are discussed.Also,the property(R)for upper triangular operator matrices is explored.
作者
赵小鹏
戴磊
曹小红
ZHAO Xiao-peng;DAI Lei;CAO Xiao-hong(School of Mathematics and Statistics,Weinan Normal University,Weinan 714099,Shaanxi,China;School of Mathematics and Statistics,Shaanxi Normal University,Xi'an 710119,Shaanxi,China)
出处
《山东大学学报（理学版）》
CAS
CSCD
北大核心
2021年第12期59-66,共8页
Journal of Shandong University(Natural Science)
基金
陕西省自然科学基金资助项目(2021JM-519)
渭南师范学院数学特色学科项目(18TSXK03)
渭南师范学院人才项目(2021RC02)。
关键词
拓扑一致降标
(R)性质
谱
topological uniform descent
property(R)
spectrum
