The stability of the single valued extension property

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. Clearly the point spectrum of any operator which has empty interior must have the single valued extension property. Using the induced spectrum of “consistent in Fredholm and index”, we investigate the stability of single valued extension property under compact perturbations, and we characterize those operators for which the single valued extension property is stable under compact perturbations.