有界线性算子及其函数的Browder定理的判定
Judgement of Browder's Theorem for Bounded Linear Operators and Their Functions
白珍贵 1曹小红2
作者信息
- 1. 陕西师范大学数学与统计学院,陕西 西安 710062;南阳市第一中学校,河南 南阳 473000
- 2. 陕西师范大学数学与统计学院,陕西 西安 710062
- 折叠
摘要
令H是无限维的Hilbert空间,B(H)是H上有界线性算子的全体构成的集合.称算子T ∈ B(H)满足Browder定理,若σ(T)\ σw(T)⊆π00(T)或σw(T)=σb(T),其中 σ(T),σw(T),σb(T)分别表示算子 T 的谱集、Weyl 谱、Browder谱,π00(T)={λ∈ isoσ(T):0＜dimN(T-λI)＜∞}.借助新的谱集,给出有界线性算子及其函数满足Browder定理的等价条件.
Abstract
Let H be an infinite dimensional Hilbert space and B(H)be the algebra of all bounded linear operators on H.T ∈ B(H)satisfies the Browder's theorem if σ(T)\ σw(T)⊆π00(T)or σw(T)=σb(T),where σ(T),σw(T),σb(T)denote the spectrum,Weyl spectrum,Browder spectrum,and π00(T)={λ ∈ isoσ(T):0＜dimN(T-λI)＜∞}.In this paper,we establish for bounded linear operators and their functions the equivalent conditions for which Browder's theorem holds by a new spectrum.
关键词
Browder定理/谱/算子函数Key words
Browder's theorem/spectrum/operator function引用本文复制引用
出版年
2024
NETL
NSTL
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