Israel Journal of Mathematics

, Volume 138, Issue 1, pp 253–270 | Cite as

First Borel class sets in Banach spaces and the asymptotic-norming property



The Radon-Nikodým property in a separable Banach spaceX is related to the representation ofX as a weak* first Borel class subset of some dual Banach space (its bidualX**, for instance) by well known results due to Edgar and Wheeler [8], and Ghoussoub and Maurey [9, 10, 11]. The generalizations of those results depend on a new notion of Borel set of the first class “generated by convex sets” which is more suitable to deal with non-separable Banach spaces. The asymptotic-norming property, introduced by James and Ho [13], and the approximation by differences of convex continuous functions are also studied in this context.


Banach Space Separable Banach Space Symmetric Convex Baire Space Pointwise Limit 
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Copyright information

© The Hebrew University Magnes Press 2003

Authors and Affiliations

  • M. Raja
    • 1
  1. 1.Departamento de MatemáticasUniversidad de Murcia Campus de EspinardoEspinardo, MurciaSpain

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