The dual of the Bourgain-Delbaen space

1998/05/31 by Dale Alspach
Mathematics · #math.FA #math.LO #msc:46B20

paper · pdf

published as Israel J. Math 117 (2000), 239-259 · 20 pages, LaTeX2e, Missing omegas in the statement and proof of Corollary 3.11 inserted

arxiv created 2003/09/26 · arxiv updated 2009/11/30

Abstract

It is shown that a script L_infty-space with separable dual constructed by Bourgain and Delbaen has small Szlenk index and thus does not have a quotient isomorphic to C(omega^omega). It follows that this is a script L_infty-space which is the same size as c₀ in the sense of the Szlenk index but does not contain c₀. This has some consequences in the theory of uniform homeomorphism of Banach spaces.

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