The single valued extension property on a Banach space

James Kenneth Finch

Vol. 58 (1975), No. 1, 61–69

DOI: 10.2140/pjm.1975.58.61

Abstract

An operator T which maps a Banach space X into itself has the single valued extension property if the only analytic function f which satisfies (λI − T)f(λ) = 0 is f = 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 λ₀I − T is semi-Fredholm and λ₀ is an interior point of the point spectrum of T, then T does not have the single valued extension property.

Mathematical Subject Classification 2000

Primary: 47B40

Milestones

Received: 17 July 1974

Published: 1 May 1975