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反对角算子矩阵及其平方的(ω)性质的摄动
引用本文:崔苗苗,曹小红,王碧玉.反对角算子矩阵及其平方的(ω)性质的摄动[J].数学学报,2016,59(3):411-420.
作者姓名:崔苗苗  曹小红  王碧玉
作者单位:陕西师范大学数学与信息科学学院 西安 710062
基金项目:国家自然科学基金资助项目(11371012, 11471200, 11571213);陕西师范大学中央高校基本科研业务费专项资金资助(GK201301007, GK201601004)
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_a(T)\σ_(ea)(T)=π_(00)(T),则称T∈B(H)满足(ω)性质,其中σ_a(T)和σ_(ea)(T)分别表示算子T的逼近点谱和本质逼近点谱,π_(00)(T)={λ∈isoσ(T):0dimN(T-λI)∞}.T∈B(H)称为满足(ω)性质的摄动,若对任意的紧算子K,T+K满足(ω)性质.本文证明了反对角算子矩阵及其平方具有(ω)性质的摄动的等价性.

关 键 词:(ω)性质  紧摄动    反对角算子矩阵

The Perturbation of Property (ω) for Anti-Diagonal Operator Matrices and Its Square
Miao Miao CUI,Xiao Hong CAO,Bi Yu WANG.The Perturbation of Property (ω) for Anti-Diagonal Operator Matrices and Its Square[J].Acta Mathematica Sinica,2016,59(3):411-420.
Authors:Miao Miao CUI  Xiao Hong CAO  Bi Yu WANG
Institution:College of Mathematics and Information Science, Shaanxi Normal University, Xi'an 710062, P. R. China
Abstract:Let H be an infinite dimensional separable complex Hilbert space and B(H) the algebra of all bounded linear operators on H.T∈B(H) satisfies Property (ω) if σa(T)\σea(T)=π00(T),where σa(T) and σea(T) denote the approximate point spectrum and essential approximate point spectrum of T respectively,π00(T)={λ∈iso σ(T):0N (T-λI)<∞}.T∈B(H) is said to have the perturbation of Property (ω) if T+K satisfies Property (ω) for all compact operator K∈B(H).We prove the equivalence of the perturbation of Property (ω) for anti-diagonal operator matrix and its square.
Keywords:Property (ω)  compact perturbations  spectrum  anti-diagonal operator matrices  
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