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Some interpolation results that are the exclusive property of compact operators

Published online by Cambridge University Press:  12 July 2007

Fernando Cobos
Departamento de Análisis Matemático, Facultad de Matemáticas, Universidad Complutense de Madrid 28040 Madrid, Spain (
Luz M. Fernández-Cabrera
Sección Departamental de Matemática Aplicada, Escuela de Estadística, Universidad Complutense de Madrid 28040 Madrid, Spain (
Antón Martínez
Departamento de Matemática Aplicada, ETS Ingenieros Industriales, Universidad de Vigo, 36200 Vigo, Spain (
Evgeniy Pustylnik
Department of Mathematics, Technion-Israel Institute of Technology, Haifa 32000, Israel (


We show that certain interpolation results for compact operators established by Cobos and co-workers cannot be extended to general closed operator ideals. We shall also characterize compactness of an embedding in terms of functions related to the classical K- and J-functionals of interpolation theory.

Research Article
Copyright © Royal Society of Edinburgh 2002

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