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Extension of smooth subspaces in Lindenstrauss spaces

Volume 222 / 2014

V. P. Fonf, P. Wojtaszczyk Studia Mathematica 222 (2014), 157-163 MSC: Primary 46B20. DOI: 10.4064/sm222-2-3

Abstract

It follows from our earlier results [Israel J. Math., to appear] that in the Gurariy space $G$ every finite-dimensional smooth subspace is contained in a bigger smooth subspace. We show that this property does not characterise the Gurariy space among Lindenstrauss spaces and we provide various examples to show that $C(K)$ spaces do not have this property.

Authors

  • V. P. FonfDepartment of Mathematics
    Ben-Gurion University of the Negev
    P.O. Box 653
    Beer-Sheva 84105, Israel
    e-mail
  • P. WojtaszczykInterdisciplinary Centre for Mathematical
    and Computational Modelling
    University of Warsaw
    Prosta 69
    02-838 Warszawa, Poland
    and
    Institute of Mathematics
    Polish Academy of Sciences
    Śniadeckich 8
    00-656 Warszawa, Poland
    e-mail

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