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Extensions of multilinear operators and Banach space properties

Published online by Cambridge University Press:  12 July 2007

Joaquín M. Gutiérrez  and
Ignacio Villanueva
Joaquín M. Gutiérrez
Affiliation:
Departamento de Matemáticas, ETS de Ingenieros Industriales, Universidad Politécnica de Madrid, C. José Gutiérrez Abascal 2, 28006 Madrid, Spain (gutierrezj@member.ams.org)
Ignacio Villanueva
Affiliation:
Departamento de Análisis Matemático, Facultad de Matemáticas, Universidad Complutense de Madrid, 28040 Madrid, Spain (ignaciov@mat.ucm.es)
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Abstract

A new characterization of the Dunford–Pettis property in terms of the extensions of multilinear operators to the biduals is obtained. For the first time, multilinear characterizations of the reciprocal Dunford–Pettis property and Pełczyński's property (V) are also found. Polynomial and holomorphic versions of these properties are given as well.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 133 , Issue 3 , June 2003 , pp. 549 - 566
Copyright
Copyright © Royal Society of Edinburgh 2003

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