Estimation of the Szlenk index of reflexive Banach spaces using generalized Baernstein spaces
Volume 228 / 2015
Fundamenta Mathematicae 228 (2015), 153-171
MSC: Primary 46B03; Secondary 46B06.
DOI: 10.4064/fm228-2-3
Abstract
For each ordinal $\alpha <\omega _1$, we prove the existence of a separable, reflexive Banach space $W$ with a basis so that $ {\rm Sz}(W), {\rm Sz}(W^*)\leq \omega ^{\alpha +1}$ which is universal for the class of separable, reflexive Banach spaces $X$ satisfying ${\rm Sz}(X), {\rm Sz}(X^*)\leq \omega ^\alpha $.
