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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