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Integral and S-factorizable multilinear mappings

Published online by Cambridge University Press:  12 July 2007

Raffaella Cilia  and
Joaquın M. Gutiérrez
Raffaella Cilia
Affiliation:
Dipartimento di Matematica, Facoltá di Scienze, Universitá di Catania, Viale Andrea Doria 6, 95125 Catania, Italy (cilia@dmi.unict.it)
Joaquın M. Gutiérrez
Affiliation:
Departamento de Matemática Aplicada, ETS de Ingenieros Industriales, Universidad Politécnica de Madrid, C. José Gutiérrez Abascal 2, 28006 Madrid, Spain (jgutierrez@etsii.upm.es)
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Abstract

We prove that several definitions of integral multilinear mappings given in the literature are equivalent. We show that what we call S-factorizable multilinear mappings are integral, but that the converse is not true (contrary to earlier claims). Using S-factorizable polynomials we give characterizations of L∞-spaces, Asplund spaces, spaces not containing ℓ1 and spaces with the compact range property. Some of these characterizations seem to be new even for linear operators.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 136 , Issue 1 , February 2006 , pp. 115 - 137
Copyright
Copyright © Royal Society of Edinburgh 2006

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