Quotients of Banach Spaces with the Daugavet Property

Tom 56 / 2008

Vladimir Kadets, Varvara Shepelska, Dirk Werner Bulletin Polish Acad. Sci. Math. 56 (2008), 131-147 MSC: Primary 46B04; Secondary 46B03, 46B25, 47B38. DOI: 10.4064/ba56-2-5

Streszczenie

We consider a general concept of Daugavet property with respect to a norming subspace. This concept covers both the usual Daugavet property and its weak$^*$ analogue. We introduce and study analogues of narrow operators and rich subspaces in this general setting and apply the results to show that a quotient of $L_1[0,1]$ by an $\ell_1$-subspace need not have the Daugavet property. The latter answers in the negative a question posed to us by A. Pełczyński.

Autorzy

  • Vladimir KadetsDepartment of Mechanics and Mathematics
    Kharkov National University
    pl. Svobody 4
    61077 Kharkov, Ukraine
    e-mail
  • Varvara ShepelskaDepartment of Mechanics and Mathematics
    Kharkov National University
    pl. Svobody 4
    61077 Kharkov, Ukraine
    e-mail
  • Dirk WernerDepartment of Mathematics
    Freie Universität Berlin
    Arnimallee 6
    D-14195 Berlin, Germany
    e-mail

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