The dual of the Bourgain-Delbaen space
Abstract
Description
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 c_0 in the sense of the Szlenk index but does not contain c_0. This has some consequences in the theory of uniform homeomorphism of Banach spaces.
20 pages, LaTeX2e, Missing omegas in the statement and proof of Corollary 3.11 inserted
20 pages, LaTeX2e, Missing omegas in the statement and proof of Corollary 3.11 inserted