广义Kato分解及单值延拓性质的摄动

Generalized Kato decomposition and perturbations of the single-valued extension property

利用与广义Kato分解有关的谱,研究单值延拓性质在紧摄动下的稳定性.此外,研究2×2上三角算子矩阵的单值延拓性质在紧摄动下的稳定性.

A Hilbert space operator T has the single-valued extension property if the only analytic function f which satisfies （ T- AI）f（A ） = 0 is f=-- 0. Obviously the point spectrum of any operator which has empty interior must have the single-valued extension property. Using the spectrum derived from ＂ generalized Kato decomposition ＂, we investigate stability of the single-valued extension property under compact perturbations. Also, we characterize the 2 × 2 upper triangular operator matrix for which the single-valued extension property is stable under compact perturbations.