Abstract:

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.

Key words: strictly generalized Kato decomposition, single valued extension property, Weyl type theorem