Banach Spaces of Bounded Szlenk Index II

Details Banach Spaces of Bounded Szlenk Index II Banach Spaces of Bounded Szlenk Index II

2008-09-22

arxiv.org/abs/0809.3626v1

Mathematics

Functional Analysis

Scientific paper

For every $\alpha<\omega_1$ we establish the existence of a separable Banach space whose Szlenk index is $\omega^{\alpha\omega+1}$ and which is universal for all separable Banach spaces whose Szlenk-index does not exceed $\omega^{\alpha\omega}$. In order to prove that result we provide an intrinsic characterization of which Banach spaces embed into a space admitting an FDD with upper estimates.

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