算子函数演算的Wey1定理
发布时间：2019-04-02 15:54
【摘要】：设H为复的无限维可分的Hilbert空间,B(H)为H上的有界线性算子的全体。若σ(T)\σ_w(T)=π00(T),则称T∈B(H)满足Weyl定理,其中σ(T)和σ_w(T)分别表示算子T的谱和Weyl谱,π00(T)表示谱集中孤立的有限重特征值的全体。首先给出了Hilbert空间上有界线性算子WeylKato分解的定义,并由Weyl-Kato分解的性质定义了一种新的谱集,利用该谱集刻画了算子函数演算满足Weyl定理的充要条件。
[Abstract]:Let H be a complex infinite dimensional separable Hilbert space, B (H) be the whole of bounded linear operators on H. If 蟽 (T)\ 蟽 _ w (T) = 蟺 00 (T), then it is said that T? B (H) satisfies Weyl theorem, where 蟽 (T) and 蟽 _ w (T) denote the spectrum of operator T and the Weyl spectrum, respectively. 蟺 00 (T) denotes the whole of isolated finite eigenvalues in spectral sets. Firstly, the definition of WeylKato decomposition of bounded linear operators on Hilbert spaces is given, and a new spectral set is defined by the properties of Weyl-Kato decomposition. The necessary and sufficient conditions for operator function calculus to satisfy Weyl theorem are characterized by this spectral set.
【作者单位】： 陕西师范大学数学与信息科学学院;
【基金】：国家自然科学基金(11371012,11471200,11571213) 中央高校基本科研业务费专项资金(GK201601004)
【分类号】：O177
本文编号：2452689
[Abstract]:Let H be a complex infinite dimensional separable Hilbert space, B (H) be the whole of bounded linear operators on H. If 蟽 (T)\ 蟽 _ w (T) = 蟺 00 (T), then it is said that T? B (H) satisfies Weyl theorem, where 蟽 (T) and 蟽 _ w (T) denote the spectrum of operator T and the Weyl spectrum, respectively. 蟺 00 (T) denotes the whole of isolated finite eigenvalues in spectral sets. Firstly, the definition of WeylKato decomposition of bounded linear operators on Hilbert spaces is given, and a new spectral set is defined by the properties of Weyl-Kato decomposition. The necessary and sufficient conditions for operator function calculus to satisfy Weyl theorem are characterized by this spectral set.
【作者单位】： 陕西师范大学数学与信息科学学院;
【基金】：国家自然科学基金(11371012,11471200,11571213) 中央高校基本科研业务费专项资金(GK201601004)
【分类号】：O177
【相似文献】
相关期刊论文 前1条
1 路干亭;;关于Wey1定理[J];陕西师范大学学报(自然科学版);1982年00期
相关博士学位论文 前1条
1 戴磊;Wey1型定理的判定及其稳定性[D];陕西师范大学;2013年
相关硕士学位论文 前1条
1 李娜娜;算子与其共轭的Wey1型定理的等价性判定[D];陕西师范大学;2012年
，本文编号：2452689
本文链接：https://www.wllwen.com/kejilunwen/yysx/2452689.html
