有界线性算子的Weyl定理的判定

O177.2; 令H为无限维复可分的Hilbert空间,B(H)为H上有界线性算子的全体,若 σ(T)\σw(T)?π00(T)或σw(T)=σb(T),称算子T∈B(H)满足Browder定理;若σ(T)\σw(T)=π00(T),称T满足Weyl定理;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)＜∞}.研究了算子及其函数的Weyl定理,给出了算子及其函数满足Weyl定理的判定方法,并讨论了相应谱集的谱映射定理....

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Published in浙江大学学报（理学版） Vol. 47; no. 5; pp. 541 - 553
Main Authors 王静, 曹小红
Format Journal Article
LanguageChinese
Published 陕西师范大学 数学与信息科学学院,陕西 西安 710062 01.09.2020
Subjects
Weyl定理
谱
Browder定理
Online AccessGet full text
ISSN1008-9497
DOI10.3785/j.issn.1008-9497.2020.05.004

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Abstract O177.2; 令H为无限维复可分的Hilbert空间,B(H)为H上有界线性算子的全体,若 σ(T)\σw(T)?π00(T)或σw(T)=σb(T),称算子T∈B(H)满足Browder定理;若σ(T)\σw(T)=π00(T),称T满足Weyl定理;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)＜∞}.研究了算子及其函数的Weyl定理,给出了算子及其函数满足Weyl定理的判定方法,并讨论了相应谱集的谱映射定理.
AbstractList O177.2; 令H为无限维复可分的Hilbert空间,B(H)为H上有界线性算子的全体,若 σ(T)\σw(T)?π00(T)或σw(T)=σb(T),称算子T∈B(H)满足Browder定理;若σ(T)\σw(T)=π00(T),称T满足Weyl定理;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)＜∞}.研究了算子及其函数的Weyl定理,给出了算子及其函数满足Weyl定理的判定方法,并讨论了相应谱集的谱映射定理.
Author 王静
曹小红
AuthorAffiliation 陕西师范大学 数学与信息科学学院,陕西 西安 710062
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WANG Jing
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Snippet O177.2; 令H为无限维复可分的Hilbert空间,B(H)为H上有界线性算子的全体,若 σ(T)\σw(T)?π00(T)或σw(T)=σb(T),称算子T∈B(H)满足Browder定理;若σ(T)\σw(T)=π00(T),称T满...
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