摘要
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.
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
Supported by the Fundamental Research Funds for the Central Universities(Grant No.GK201301007)
National Natural Science Foundation of China(Grant No.11371012)