Representation of operators with martingales and the Radon-Nikodým property

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

     Universidad de Oviedo

     Oviedo, España

     
• Localización: Extracta mathematicae, ISSN-e 0213-8743, Vol. 19, Nº 1, 2004 (Ejemplar dedicado a: V Curso sobre espacios de Banach y operadores), págs. 135-140
• Idioma: inglés
• Títulos paralelos:
  • Representación de operadores con martingalas y la propiedad de Radon-Nikodym
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• Resumen

  • The Radon-Nikodým property was introduced to describe those Banach spaces X for which all operators acting between L1 and X have a representation function. These spaces can be characterized in terms of martingales, as those spaces in which every uniformly bounded martingale converges. In the present work we study some classes of operators defined upon their behaviour with respect to the convergence of such martingales. We prove that an operator preserves the non-convergence of uniformly bounded martingales if and only if all its compact perturbations have Asplund cokernel.