%0 Journal Article
%T 算子立方的Weyl定理及其紧摄动<br>Weyls theorem for the cube of operator and compact perturbations
%A 董炯
%A 曹小红&lt
%A br&gt
%A DONG Jiong
%A CAO Xiao-hong
%J 山东大学学报（理学版）
%D 2016
%R 10.6040/j.issn.1671-9352.0.2015.530
%X 摘要： 若σ(T)\σw(T)=π00(T), 则称T∈B(H)满足Weyl定理。 T∈B(H)满足Weyl定理的紧摄动: 如果对任意的紧算子K∈B(H), T+K都满足Weyl定理。本文给出了一种Weyl谱的变体, 根据该变体讨论了T 3和T满足Weyl定理的紧摄动的关系。<br>Abstract: An operator T∈B(H) is said to satisfy Weyls theorem if σ(T)\σw(T)=π00(T). T∈B(H) is said to have the compact perturbations of Weyls theorem if T+K satisfies Weyls theorem for all compact operators K∈B(H). In this note, a variant of the Weyl spectrum is discussed. Using the variant, we characterize the conditions for T 3 and T satisfying the compact perturbations of Weyls theorem
%K Weyl定理
%K Weyl-Kato分解
%K 紧摄动
%K &lt
%K br&gt
%K Weyls theorem
%K compact perturbations
%K Weyl-Kato decomposition
%U http://lxbwk.njournal.sdu.edu.cn/CN/10.6040/j.issn.1671-9352.0.2015.530