Banach spaces of bounded Szlenk index

E. Odell; Th. Schlumprecht; A. Zsák

Studia Mathematica, Tome 178 (2007), p. 63-97 / Harvested from The Polish Digital Mathematics Library

Résumé

For a countable ordinal α we denote by $_{α}$ the class of separable, reflexive Banach spaces whose Szlenk index and the Szlenk index of their dual are bounded by α. We show that each $_{α}$ admits a separable, reflexive universal space. We also show that spaces in the class $_{ω^{α \cdot ω}}$ embed into spaces of the same class with a basis. As a consequence we deduce that each $_{α}$ is analytic in the Effros-Borel structure of subspaces of C[0,1].

Publié le : 2007-01-01

Zbl 1138.46005

EUDML-ID : urn:eudml:doc:284580

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     title = {Banach spaces of bounded Szlenk index},
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     year = {2007},
     pages = {63-97},
     zbl = {1138.46005},
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E. Odell; Th. Schlumprecht; A. Zsák. Banach spaces of bounded Szlenk index. Studia Mathematica, Tome 178 (2007) pp. 63-97. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm183-1-4/