Narrow operators and rich subspaces of Banach spaces with the Daugavet property

Volume 147 / 2001

Vladimir M. Kadets, Roman V. Shvidkoy, Dirk Werner Studia Mathematica 147 (2001), 269-298 MSC: Primary 46B20; Secondary 46B04, 47B38. DOI: 10.4064/sm147-3-5

Abstract

Let $X$ be a Banach space. We introduce a formal approach which seems to be useful in the study of those properties of operators on $X$ which depend only on the norms of the images of elements. This approach is applied to the Daugavet equation for norms of operators; in particular we develop a general theory of narrow operators and rich subspaces of spaces $X$ with the Daugavet property previously studied in the context of the classical spaces $C(K)$ and $L_{1}(\mu )$.

Authors

  • Vladimir M. KadetsFaculty of Mechanics and Mathematics
    Kharkov National University
    pl. Svobody 4, 61077 Kharkov, Ukraine
    Current address
    Department of Mathematics
    Freie Universität Berlin
    Arnimallee 2–6
    D-14195 Berlin, Germany
    e-mail
    e-mail
  • Roman V. ShvidkoyDepartment of Mathematics
    University of Missouri
    Columbia, MO 65211, U.S.A.
    e-mail
  • Dirk WernerDepartment of Mathematics
    Freie Universität Berlin
    Arnimallee 2–6
    D-14195 Berlin, Germany
    e-mail

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