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INTERPOLATION METHODS DEFINED BY MEANS OF POLYGONS AND COMPACT OPERATORS

Published online by Cambridge University Press:  08 January 2008

Luz M. Fernández-Cabrera  and
Antón Martínez
Luz M. Fernández-Cabrera
Affiliation:
Sección Departamental de Matemática Aplicada, Escuela de Estadística, Universidad Complutense de Madrid, 28040 Madrid, Spain (luz\[email protected])
Antón Martínez
Affiliation:
Departamento de Matemática Aplicada I, Escuela Técnica Superior Ingenieros Industriales, Universidad de Vigo, 36200 Vigo, Spain ([email protected])
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Abstract

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We work with interpolation methods for $N$-tuples of Banach spaces associated with polygons. We compare necessary conditions for interpolating closed operator ideals with conditions required to interpolate compactness. We also establish a formula for the measure of non-compactness of interpolated operators.

Keywords

Primary 46B7047B10interpolation methods associated with polygonscompact operatorsclosed operator idealsmeasure of non-compactness
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 50 , Issue 3 , October 2007 , pp. 653 - 671
Copyright
Copyright © Edinburgh Mathematical Society 2007