J. Aust. Math. Soc.  76 (2004), 269-280
Nuclear and integral polynomials

Raffaella Cilia
  Dipartimento di Matematica
  Facoltà di Scienze
  Università di Catania
  Viale Andrea Doria 6
  95100 Catania
  Italy
  cilia@dmi.unict.it
and
Joaquín M. Gutiérrez
  Departamento de Matemática Aplicada
  ETS de Ingenieros Industriales
  Universidad Politécnica de Madrid
  C. José Gutiérrez Abascal 2
  28006 Madrid
  Spain
  jgutierrez@etsii.upm.es


Abstract
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.
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