On operators that preserve the Radon-Nikodým property

• Antonio Martínez Abejón ; Miguel González Velasco ; Javier Pello-García
  1. [1] Universidad de Oviedo

     Universidad de Oviedo

     Oviedo, España

     
• Localización: Extracta mathematicae, ISSN-e 0213-8743, Vol. 22, Nº 2, 2007 (Ejemplar dedicado a: Banach space theory: classical topics and new directions. Cáceres 2006), págs. 191-196
• Idioma: inglés
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• Resumen

  • We consider a certain class RN+ of operators that preserve the Radon-Nikod´ym property. Conjugate operators in RN+ can be characterized as those operators T such that the kernel N(T+K) has the Radon-Nikod´ym property for every compact operator K. A construction by J. Bourgain involving infinite convolution products of measures in the Cantor group provides examples of operators T : L1 ! L1 in the class RN+. As an application, we show the existence of Banach spaces which are L1-spaces, have the Radon- Nikod´ym property and contain infinite-dimensional reflexive subspaces