算子立方的Weyl定理及其紧摄动

Weyl's theorem for the cube of operator and compact perturbations

若σ(T)\σ_w(T)=π_(00)(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T3和T满足Weyl定理的紧摄动的关系。

An operator T∈B( H) is said to satisfy Weyl's theorem if σ( T) \ σ_w( T) = π_(00)( 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 T3 and T satisfying the compact perturbations of Weyl's theorem.