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Radon-Nikodým compact spaces and fragmentability

Part of: Normed linear spaces and Banach spaces; Banach lattices

Published online by Cambridge University Press:  26 February 2010

I. Namioka
I. Namioka
Affiliation:
Department of Mathematics, GN-50, University of Washington, Seattle, Washington 98195, U.S.A.
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Extract

While investigating Asplund spaces in [15], R. R. Phelps and the author noticed that weak* compact subsets of the duals of Asplund spaces (or equivalently, as it turned out, weak* compact subsets of dual Banach spaces with the Radon-Nikodým property) possessed many properties in common with weakly compact subsets of Banach spaces. The topological study of the spaces homeomorphic to the latter, the so-called Eberlein compact spaces, or EC spaces for short, had flourished and had already yielded a rich collection of results. Therefore it was natural to hope that a similar study of the former might also lead to interesting discoveries. In a series of letters with S. Fitzpatrick exchanged during the summer and the fall of 1981, we started to collect properties of compact spaces that are homeomorphic to weak* compact subsets of the duals of Asplund spaces, which we tentatively called “Asplund compact spaces“. However, as far as we are aware, Reynov's paper [16] is the first study in print of the topological properties of “Asplund compact spaces” or “compacta of RN type” as Reynov termed them.

MSC classification

Secondary: 46B22: Radon-Nikodým, Kreĭn-Milman and related properties
Type
Research Article
Information
Mathematika , Volume 34 , Issue 2 , December 1987 , pp. 258 - 281
Copyright
Copyright © University College London 1987

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