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- 2016
算子立方的Weyl定理及其紧摄动
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Abstract:
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。
Abstract: An operator T∈B(H) is said to satisfy Weyls theorem if σ(T)\σw(T)=π00(T). T∈B(H) is said to have the compact perturbations of Weyls theorem if T+K satisfies Weyls 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 Weyls theorem
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