[1]杨国增,孔莹莹,曹小红.有界线性算子的a-Weyl定理及亚循环性[J].深圳大学学报理工版,2017,34(No.4(331-440)):372-377.[doi:10.3724/SP.J.1249.2017.04372]
 Yang Guozeng,Kong Yingying,and Cao Xiaohong.A-Weyl’s theorem and hypercyclic property for bounded linear operators[J].Journal of Shenzhen University Science and Engineering,2017,34(No.4(331-440)):372-377.[doi:10.3724/SP.J.1249.2017.04372]
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有界线性算子的a-Weyl定理及亚循环性()
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《深圳大学学报理工版》[ISSN:1000-2618/CN:44-1401/N]

卷:
第34卷
期数:
2017年No.4(331-440)
页码:
372-377
栏目:
数学与应用数学
出版日期:
2017-07-10

文章信息/Info

Title:
A-Weyl’s theorem and hypercyclic property for bounded linear operators
文章编号:
201704006
作者:
杨国增1孔莹莹2曹小红2
1)郑州师范学院数学与统计学院,河南郑州 450044
2)陕西师范大学数学与信息科学学院,陕西西安710062
Author(s):
Yang Guozeng1 Kong Yingying2 and Cao Xiaohong2
1)School of Mathematics and Statistics, Zhengzhou Normal University, Zhengzhou 450044, Henan Province, P.R.China;
2) Shaanxi Normal University, Institute of Mathematics and Information Science, Xi’an 710062, Shaanxi Province, P.R.China
关键词:
线性算子理论a-Weyl定理逼近点谱亚循环算子算子函数Fredholm算子谱集Browder谱
Keywords:
linear operator theory a-Weyl’s theorem approximate point spectrum hypercyclic operators operator function Fredholm operator spectrum set Browder spectrum
分类号:
O 177.2
DOI:
10.3724/SP.J.1249.2017.04372
文献标志码:
A
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.称T∈B(H)满足a-Weyl定理,若σa(T)\σea(T)=πa00(T), 其中, σa(T)和σea(T)分别表示算子T∈B(H)的逼近点谱和本质逼近点谱, πa00(T)={λ∈isoσa(T)∶0<dim N(T-λI)<∞}. 通过定义新的谱集,给出了算子函数满足a-Weyl定理的判定方法,研究了当T为亚循环算子时, 算子函数满足a-Weyl定理的充要条件.
Abstract:
Let H be an infinite dimensional separable complex Hilbert space and B(H) be the algebra of all bounded linear operators on H. For T∈B(H), we call a-Weyl’s theorem holds for T if σa(T)\σea(T)=πa00(T), where σa(T) and σea(T) denote the approximate point spectrum and essential approximate point spectrum respectively, and πa00(T)={λ∈isoσa(t)∶0<dim N(T-λI)<∞}. Using the new defined spectrum, we investigate a-Weyl’s theorem for operator function. Meanwhile, we characterize the sufficient and necessary conditions for operator function satisfying a-Weyl’s theorem if T is a hypercyclic operator.

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备注/Memo

备注/Memo:
Received:2016-12-22;Accepted:2017-04-18
Foundation:National Natural Science Foundation of China (11471200)
Corresponding author:Professor Cao Xiaohong. E-mail: xiaohongcao@snnu.edu.cn
Citation:Yang Guozeng, Kong Yingying, Cao Xiaohong. A-Weyl’s theorem and hypercyclic property for bounded linear operators[J]. Journal of Shenzhen University Science and Engineering, 2017, 34(4): 372-377.(in Chinese)
基金项目:国家自然科学基金资助项目(11471200)
作者简介:杨国增(1980—),男,郑州师范学院讲师.研究方向:泛函算子理论.E-mail:ygz_0907@163.com
引文:杨国增,孔莹莹,曹小红.有界线性算子的a-Weyl定理及亚循环性[J]. 深圳大学学报理工版,2017,34(4):372-377.
更新日期/Last Update: 2017-06-26