A bounded linear operator T acting on a Hilbert space is called Coburn operator if ker(T-λ) = {0} or ker(T-λ)*= {0} for each λ∈ C. In this paper, the authors define other Coburn type properties for Hilbert space o...A bounded linear operator T acting on a Hilbert space is called Coburn operator if ker(T-λ) = {0} or ker(T-λ)*= {0} for each λ∈ C. In this paper, the authors define other Coburn type properties for Hilbert space operators and investigate the compact perturbations of operators with Coburn type properties. They characterize those operators for which has arbitrarily small compact perturbation to have some fixed Coburn property.Moreover, they study the stability of these properties under small compact perturbations.展开更多
Abstract A Hilbert space operator T is said to have property （ω1） if σα（T）／σaw（T） π00（T）, where σα（T） andσαw（T） denote the approximate point spectrum and the Weyl essential approximate point sp...Abstract A Hilbert space operator T is said to have property （ω1） if σα（T）／σaw（T） π00（T）, where σα（T） andσαw（T） denote the approximate point spectrum and the Weyl essential approximate point spectrum of T respectively, and π00（T） ---- {λ∈ iso σ（T）, 0 〈 dim N（T- λI） 〈 ∞}. Ifσα（T）／σαw（T） = π00（T）, we say T satisfies property （w）. In this note, we investigate the stability of the property （wi） and the property （w） under compact perturbations, and we characterize those operators for which the property （wi） and the property （w） are stable under compact perturbations.展开更多
设H为无限维的复可分Hilbert空间,B(H)为H上的有界线性算子的全体。设T=(A B -B A)∈B(HH)为算子矩阵。本文在Bk=0(k∈N且k≥2),AB=BA时,用A的单值延拓性质的紧摄动和Browder定理的紧摄动分别刻画了T的单值延拓性质的紧摄动和Browder...设H为无限维的复可分Hilbert空间,B(H)为H上的有界线性算子的全体。设T=(A B -B A)∈B(HH)为算子矩阵。本文在Bk=0(k∈N且k≥2),AB=BA时,用A的单值延拓性质的紧摄动和Browder定理的紧摄动分别刻画了T的单值延拓性质的紧摄动和Browder定理的紧摄动。展开更多
基金supported by the National Natural Science Foundation of China(Nos.11901035,11901230)。
文摘A bounded linear operator T acting on a Hilbert space is called Coburn operator if ker(T-λ) = {0} or ker(T-λ)*= {0} for each λ∈ C. In this paper, the authors define other Coburn type properties for Hilbert space operators and investigate the compact perturbations of operators with Coburn type properties. They characterize those operators for which has arbitrarily small compact perturbation to have some fixed Coburn property.Moreover, they study the stability of these properties under small compact perturbations.
基金Supported by the Fundamental Research Funds for the Central Universities(Grant No.GK201301007)National Natural Science Foundation of China(Grant No.11371012)
文摘Abstract A Hilbert space operator T is said to have property （ω1） if σα（T）／σaw（T） π00（T）, where σα（T） andσαw（T） denote the approximate point spectrum and the Weyl essential approximate point spectrum of T respectively, and π00（T） ---- {λ∈ iso σ（T）, 0 〈 dim N（T- λI） 〈 ∞}. Ifσα（T）／σαw（T） = π00（T）, we say T satisfies property （w）. In this note, we investigate the stability of the property （wi） and the property （w） under compact perturbations, and we characterize those operators for which the property （wi） and the property （w） are stable under compact perturbations.
基金the Natural Science Foundation of Shannxi Province(No.2021JM519)2021 Talent Project of Weinan Normal University(No.2021RC16)2022 Horizontal Project of Weinan Normal University(No.2022HX126)。
