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Nuclear and integral polynomials

Part of: Nonlinear operators and their properties Normed linear spaces and Banach spaces; Banach lattices Measures, integration, derivative, holomorphy

Published online by Cambridge University Press:  09 April 2009

Raffaella Cilia  and
Joaquín M. Gutiérrez
Raffaella Cilia
Affiliation:
Dipartimento di Matematica Facoltà di Science, Università di Catania, Viale Andrea Doria, 6 95100 Catania, Itlay e-mail: cilia@dmi.unict.it
Joaquín M. Gutiérrez
Affiliation:
Departamento de Matemática Aplicada ETS de Ingenieros IndustrialesUniversidad Politécnica de MadridC. José Gutiérrez Abascal 2 28006 Madrid, Spain e-mail: jgutierrez@etsii.upm.es
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Abstract

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Let E be a Banach space whose dual E* has the approximation property, and let m be an index. We show that E* has the Radon-Nikodým property if and only if every m-homogeneous integral polynomial from E into any Banach space is nuclear. We also obtain factorization and composition results for nuclear polynomials.

Keywords

1-dominated polynomial, integral polynonmialnuclear polynomialfactorization of polynomials

MSC classification

Secondary: 46G25: (Spaces of) multilinear mappings, polynomials 46B20: Geometry and structure of normed linear spaces 47H60: Multilinear and polynomial operators
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 76 , Issue 2 , April 2004 , pp. 269 - 280
Copyright
Copyright © Australian Mathematical Society 2004

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