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The spectrum of an interpolated operator and analytic multivalued functions

1986; Mathematical Sciences Publishers; Volume: 121; Issue: 2 Linguagem: Inglês

10.2140/pjm.1986.121.445

1945-5844

Thomas Ransford,

Analytic and geometric function theory

Let [B o , B λ ] be a complex interpolation pair and T: B o + B x -* B o + B 1 be a linear map whose restriction to each interpolation space [B O ,B 1 ] S is a bounded operator on that space with spectrum Sp s T.Under mild conditions on T it is shown that the set-valued map λ -> Sp (Reλ) Γ is an analytic multivalued function.This fact is used to unify and generalise a number of previously known results about the spectrum of an interpolated operator, and also to motivate some new ones.G. R. Allan for his helpful advice and encouragement.Part of