有界线性算子的拓扑一致降标与(R)性质

doi:10.6040/j.issn.1671-9352.0.2021.051

《山东大学学报(理学版)》 ›› 2021, Vol. 56 ›› Issue (12): 59-66.doi: 10.6040/j.issn.1671-9352.0.2021.051

• • 上一篇

有界线性算子的拓扑一致降标与(R)性质

赵小鹏¹,戴磊¹,曹小红^2*

1.渭南师范学院数学与统计学院, 陕西渭南 714099;2.陕西师范大学数学与统计学院, 陕西西安 710119

发布日期:2021-11-25
作者简介:赵小鹏(1968— ),男,硕士,副教授,研究方向为算子理论与算子代数. E-mail:zxp@wnu.edu.cn *通信作者简介:曹小红(1972— ),女,教授,博士生导师,研究方向为算子理论与算子代数. E-mail:xiaohongcao@snnu.edu.cn
基金资助:
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)

Topological uniform descent and property (R) for bounded linear operators

ZHAO Xiao-peng¹, DAI Lei¹, CAO Xiao-hong^2*

1. School of Mathematics and Statistics, Weinan Normal University, Weinan 714099, Shaanxi, China;
2. School of Mathematics and Statistics, Shaanxi Normal University, Xian 710119, Shaanxi, China

Published:2021-11-25

摘要/Abstract

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σa(T)\σ_ab(T)=π₀₀(T),其中σa(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,π₀₀(T)={λ∈iso σ(T):0<dim N(T-λI)<∞}。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。

关键词: 拓扑一致降标, (R)性质, 谱

Abstract: 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) if σ_a(T)\σ_ab(T)=π00(T), where σ_a(T) and σab(T)denote the approximate point spectrum and the Browder essential approximate point spectrum of T respectively, and π00(T)={λ∈iso σ(T):0N(T-λI)<∞}. 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.

Key words: topological uniform descent, property (R), spectrum

中图分类号:

O177.2

赵小鹏,戴磊,曹小红. 有界线性算子的拓扑一致降标与(R)性质[J]. 《山东大学学报(理学版)》, 2021, 56(12): 59-66.

ZHAO Xiao-peng, DAI Lei, CAO Xiao-hong. Topological uniform descent and property (R) for bounded linear operators[J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2021, 56(12): 59-66.

参考文献

[1] WEYL H V. Über beschränkte quadratische formen, deren differenz vollstetig ist[J]. Rendiconti Del Circolo Matematico Di Palermo, 1909, 27(1):373-392.
[2] HARTE R, LEE W Y. Another note on Weyls theorem[J]. Transactions of the American Mathematical Society, 1997, 349(5):2115-2124.
[3] RAKO CEVIC V. Operators obeying a-Weyls theorem[J]. Revue Roumaine des Mathematiques Pures et Appliquees, 1989, 34(10):915-919.
[4] RAKO CEVIC V. On a class of operators[J]. Matematicki Vesnik, 1985, 37(4):423-426.
[5] AIENA P, GUILLÉN J R, PEÑA P. Property (R) for bounded linear operators[J]. Mediterranean Journal of Mathematics, 2011, 8(4):491-508.
[6] AIENA P, APONTE E, GUILLÉN J R, et al. Property(R) under perturbations[J]. Mediterranean Journal of Mathematics, 2013, 10(1):367-382.
[7] JIA Boting,FENG Youling. Property(R)under compact perturbations[J]. Mediterranean Journal of Mathematics, 2020, 17(2):491-508.
[8] GRABINER S. Uniform ascent and descent of bounded operaters[J]. Journal of the Mathematical Society of Japan, 1982, 34(2):317-337.
[9] RADJAVI H, ROSENTHAL P. Invariant subspaces[M]. 2nd ed. Mineola: Dover Publications, 2003.
[10] DONG Jiong, CAO Xiaohong. Compact perturbations of both SVEP and Weyls theorem for 3×3 upper triangular operator matrices[J]. Linear and Multilinear Algebra, 2020, 68(10):2020-2033.
[11] DONG Jiong, CAO Xiaohong. The(generalized)Weylness of upper triangular operator matrices[J]. Analysis Mathematica, 2020, 46(3):465-481.
[12] CUI Miaomiao, CAO Xiaohong. Weyls theorem for upper triangular operator matrix and perturbations[J]. Linear and Multilinear Algebra, 2018, 66(7):1-12.

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有界线性算子的拓扑一致降标与(R)性质

Topological uniform descent and property (R) for bounded linear operators

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