Geodesic
Narrow operators and rich subspaces of Banach spaces with the Daugavet property
Vladimir M. Kadets1 ; Roman V. Shvidkoy2 ; Dirk Werner3
1 Faculty 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
2 Department of Mathematics University of Missouri Columbia, MO 65211, U.S.A.
3 Department of Mathematics Freie Universität Berlin Arnimallee 2–6 D-14195 Berlin, Germany
Studia Mathematica, Tome 147 (2001) no. 3, pp. 269-298

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

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 $L_{1}(\mu )$.
DOI : 10.4064/sm147-3-5
Keywords: banach space introduce formal approach which seems useful study those properties operators which depend only norms images elements approach applied daugavet equation norms operators particular develop general theory narrow operators rich subspaces spaces daugavet property previously studied context classical spaces

Vladimir M. Kadets 1 ; Roman V. Shvidkoy 2 ; Dirk Werner 3

1 Faculty 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
2 Department of Mathematics University of Missouri Columbia, MO 65211, U.S.A.
3 Department of Mathematics Freie Universität Berlin Arnimallee 2–6 D-14195 Berlin, Germany 
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Vladimir M. Kadets; Roman V. Shvidkoy; Dirk Werner. Narrow operators and rich subspaces of
Banach spaces with the Daugavet property. Studia Mathematica, Tome 147 (2001) no. 3, pp. 269-298. doi: 10.4064/sm147-3-5

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