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Spectrum of interpolated operators

Albrecht, Ernst ; Müller, Vladimir

Proceedings of the American Mathematical Society, 2001-03, Vol.129 (3), p.807-814 [Periódico revisado por pares]

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Título:
Spectrum of interpolated operators
Autor: Albrecht, Ernst ; Müller, Vladimir
Assuntos: Banach space ; Hilbert spaces ; Interpolation ; Linear transformations ; Mathematical functions ; Operator theory ; Polynomials ; Separable spaces ; Subharmonics
É parte de: Proceedings of the American Mathematical Society, 2001-03, Vol.129 (3), p.807-814
Descrição: Let (X_0,X_1) be a compatible pair of Banach spaces and let T be an operator that acts boundedly on both X_0 and X_1. Let T_{[\theta]} \quad(0\le\theta\le 1) be the corresponding operator on the complex interpolation space (X_0,X_1)_{[\theta]}. The aim of this paper is to study the spectral properties of T_{[\theta]}. We show that in general the set-valued function \theta\mapsto \sigma(T_{[\theta]}) is discontinuous even in inner points \theta\in(0,1) and show that each operator satisfies the local uniqueness-of-resolvent condition of Ransford. Further we study connections with the real interpolation method.
Editor: American Mathematical Society
Idioma: Inglês

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