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

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.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 132 , Issue 2 , April 2002 , pp. 317 - 328
Copyright
Copyright © Royal Society of Edinburgh 2002

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