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Preprint No.
A-00-12
Vladimir M. Kadets, Roman V. Shvidkoy, Dirk Werner
Narrow operators and
rich subspaces of Banach spaces with the Daugavet property
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 $L_{1}(\mu)$.
Keywords: Daugavet property, Daugavet equation, rich subspace,
narrow operator
Mathematics Subject Classification (MSC91): 46B20; 46B04, 47B38
Language: ENG
Available: Pr-A-00-12.ps
Contact: Dirk Werner, Freie Universität Berlin, Fachbereich Mathematik und Informatik, Arnimallee 2-6, D-14195 Berlin, Germany (werner@math.fu-berlin.de)
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