Abstract
Let (E 0,E 1) be a compatible couple of Banach spaces, and letE λ: 0≤Reλ≤1 be the complex interpolation spaces ofE 0,E 1. LetT be a closed linear operator onE 0+E 1, then the restrictionT λ ofT to eachE λ is closed. If we denote by\(\tilde \sigma (T_\lambda )\) the extended spectrum ofT λ inE λ, then, under appropriate conditions, it is shown that the map\(\lambda \mapsto \tilde \sigma (T_\lambda )\) is an analytic multifunction in the strip {λ∈C∶0<Reλ<1}. We use these results to give some applications to the spectral theory of semigroups.
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