First Borel class sets in Banach spaces and the asymptotic-norming property
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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 , 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 , and the approximation by differences of convex continuous functions are also studied in this context.
KeywordsBanach Space Separable Banach Space Symmetric Convex Baire Space Pointwise Limit
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- A. Bellow,Lifting compact spaces, Lecture Notes in Mathematics794, Springer-Verlag, Berlin, 1980, pp. 233–253.Google Scholar
- R. D. Bourgin,Geometric Aspects of Convex Sets with Radon-Nikodým Property, Lecture Notes in Mathematics993, Springer-Verlag, Berlin, 1980.Google Scholar
- R. Deville, G. Godefroy and V. Zizler,Smoothness and Renorming in Banach Spaces, Pitman Monographs and Surveys 64, Longman Sci. Tech., Harlow, 1993.Google Scholar
- N. Ghoussoub and B. Maurey,H δ-embeddings in Hilbert space and optimization onG δ-sets, Memoirs of the American Mathematical Society349 (1986),.Google Scholar
- Z. Hu and B.-L. Lin,On the asymptotic norming property of Banach spaces, Lecture Notes in Pure and Applied Mathematics136, Dekker, New York, 1992, pp. 195–210.Google Scholar
- K. Kuratowski,Topology, Volume I, PWN Polish Scientific Publishers, Warsaw, 1966.Google Scholar
- G. Lancien,Théorie de l’indice et problèmes de renormage en géométrie des espaces de Banach, Thèse, Paris, 1992.Google Scholar