Estimation of the Szlenk index of Banach spaces via Schreier spaces

Tom 216 / 2013

Ryan Causey Studia Mathematica 216 (2013), 149-178 MSC: Primary 46B03; Secondary 46B20. DOI: 10.4064/sm216-2-4

Streszczenie

For each ordinal $\alpha <\omega _1$, we prove the existence of a Banach space with a basis and Szlenk index $\omega ^{\alpha +1}$ which is universal for the class of separable Banach spaces with Szlenk index not exceeding $\omega ^\alpha $. Our proof involves developing a characterization of which Banach spaces embed into spaces with an FDD with upper Schreier space estimates.

Autorzy

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

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