Vol. 58, No. 1, 1975

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The single valued extension property on a Banach space

James Kenneth Finch

Vol. 58 (1975), No. 1, 61–69

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
Received: 17 July 1974
Published: 1 May 1975
James Kenneth Finch