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Generalization of Zippin’s theorem on perturbing Banach spaces with separable dual

Volume 245 / 2019

P. Hájek, Th. Schlumprecht, A. Zsák Studia Mathematica 245 (2019), 169-183 MSC: Primary 46B20; Secondary 46B26. DOI: 10.4064/sm170619-30-11 Published online: 20 July 2018

Abstract

We generalize a result on Banach spaces with separable dual which was first shown by Zippin, and was explicitly formulated by Benyamini. We prove that there is a class of Asplund spaces, which includes all spaces with separable dual, whose members can be perturbed inside a suitable ambient space to be contained in the space of continuous functions on a well-founded compact tree.

Authors

  • P. HájekInstitute of Mathematics
    Czech Academy of Sciences
    Žitná 25
    115 67 Praha 1, Czech Republic
    and
    Faculty of Electrical Engineering
    Czech Technical University in Prague
    Zikova 4
    166 27 Praha, Czech Republic
    e-mail
  • Th. SchlumprechtDepartment of Mathematics
    Texas A&M University
    College Station, TX 77843, U.S.A.
    and
    Faculty of Electrical Engineering
    Czech Technical University in Prague
    Zikova 4
    166 27 Praha, Czech Republic
    e-mail
  • A. ZsákPeterhouse
    Cambridge, CB2 1RD, UK
    e-mail

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