Weyl型定理与单值延拓性质的等价性

Equivalence between Weyl Type Theorem and Single Valued Extention Property

利用算子的严格广义Kato分解性质,研究算子的单值延拓性质与Weyl型定理在紧摄动下的稳定性以及Weyl型定理与单值延拓性质紧摄动之间的关系,得到了Weyl型定理摄动与单值延拓性质摄动等价的充要条件.

Using the strictly generalized Kato decomposition property of operator,we investigated the stability of the single valued extension property of the operator and the Weyl type theorem under compact perturbations.In addition,we also discussed the relation between the Weyl type theorem and the single valued extension property under compact perturbation.Then we obtained the sufficient and necessary conditions for the equivalence of the perturbation of Weyl type theorem and single valued extension property.