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Disjointly strictly singular operators and interpolation*

Published online by Cambridge University Press:  14 November 2011

A. García del Amo
Affiliation:
Departamento de Análisis Matemático, Facultad de C. Matemáticas, Universidad Complutense de Madrid, 28040 Madrid, Spain e-mail (A. García del Amo): GARCIADA@MAT.UCM.ES
F. L. Hernández
Affiliation:
Departamento de Análisis Matemático, Facultad de C. Matemáticas, Universidad Complutense de Madrid, 28040 Madrid, Spain e-mail (F. L. Hernández): PACOH@MAT.UCM.ES
C. Ruiz
Affiliation:
Departamento de Análisis Matemático, Facultad de C. Matemáticas, Universidad Complutense de Madrid, 28040 Madrid, Spain e-mail (C. Ruiz): CRUIZB@SUNAM1.MAT.UCM.ES

Abstract

Interpolation properties of the class of disjointly strictly singular operators on Banach lattices are studied. We also give some applications to compare the lattice structure of two rearrangement invariant function spaces. In particular, we obtain suitable analytic characterisations of when the inclusion map between two Orlicz function spaces is disjointly strictly singular.

Type
Research Article
Copyright
Copyright © Royal Society of Edinburgh 1996

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