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Estimation of the Szlenk index of reflexive Banach spaces using generalized Baernstein spaces

Volume 228 / 2015

Ryan Causey 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 $.

Authors

  • Ryan CauseyDepartment of Mathematics
    Texas A&M University
    College Station, TX 77845, U.S.A.
    e-mail

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