The single valued extension property on a Banach space

Abstract

An operator T which maps a Banach space X into itself has the single valued extension property if the only analytic function / which satisfies (l -)/() = 0 is / = 0. Clearly the point spectrum of any operator which does not have the single valued extension property must have nonempty interior. The converse does not hold. However, it is shown below that if o l -T is semi-Fredholm and 0 is an interior point of the point spectrum of , then T does not have the single valued extension property.