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Banach spaces of bounded Szlenk index II

Tom 205 / 2009

D. Freeman, E. Odell, Th. Schlumprecht, A. Zsák Fundamenta Mathematicae 205 (2009), 161-177 MSC: 46B20, 54H05. DOI: 10.4064/fm205-2-5

Streszczenie

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 Tsirelson type upper estimates.

Autorzy

  • D. FreemanDepartment of Mathematics
    Texas A&M University
    College Station, TX 77843, U.S.A.
    e-mail
  • E. OdellDepartment of Mathematics
    The University of Texas
    1 University Station C1200
    Austin, TX 78712, U.S.A.
    e-mail
  • Th. SchlumprechtDepartment of Mathematics
    Texas A&M University
    College Station, TX 77843, U.S.A.
    e-mail
  • A. ZsákSchool of Mathematics
    University of Leeds
    Leeds, LS2 9JT, United Kingdom
    e-mail

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