关键词: 单值延拓性质, 紧摄动, 广义Kato分解

Abstract:

A Hilbert space operator T has the single-valued extension property if the only analytic function f which satisfies (T-λI)f(λ)=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.

Key words: single-valued extension property, compact perturbation, generalized Kato decomposition