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Polynomials on banach spaces whose duals are isomorphic to ℓ1 (Γ)

Published online by Cambridge University Press:  17 April 2009

Raffaella Cilia ,
Maria D'Anna  and
Joaquín M. Gutiérrez
Raffaella Cilia
Affiliation:
Dipartimento di Matematica, Facolt` di Scienze, Università di Catania, Viale Andrea Doria 6, 95100 Catania, Italy e-mail: cilia@dmi.unict.it
Maria D'Anna
Affiliation:
Dipartimento di Matematica, Facoltà di Scienze, Università di Catania, Viale Andrea Doria 6, 95100 Catania, Italy e-mail: danna@dipmat.unict.it
Joaquín M. Gutiérrez
Affiliation:
Departamento de Matemática Aplicada, ETS de Ingenieros Industriales, Universidad Politécnica de Madrid, C. José Gutiérrez Abascal 2, 28006 Madrid, Spain e-mail: jgutierrez@etsii.upm.es
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We prove that the dual of a Banach space E is isomorphic to an ℓ1(Γ) space if and only if, for a fixed integer m, every m-homogeneous 1-dominated polynomial on E is nuclear. This extends a result for linear operators due to Lewis and Stegall. The same techniques used for this result allow us to prove that, if every m-homogeneous integral polynomial between two Banach spaces is nuclear, then every integral (linear) operator between the same spaces is nuclear.

Information

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 70 , Issue 1 , August 2004 , pp. 117 - 124
Copyright
Copyright © Australian Mathematical Society 2004

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