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# Wydawnictwa / Czasopisma IMPAN / Studia Mathematica / Wszystkie zeszyty

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

### Tom 147 / 2001

Studia Mathematica 147 (2001), 269-298 MSC: Primary 46B20; Secondary 46B04, 47B38. DOI: 10.4064/sm147-3-5

#### Streszczenie

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 $L_{1}(\mu )$.

#### Autorzy

• Vladimir M. KadetsFaculty of Mechanics and Mathematics
Kharkov National University
pl. Svobody 4, 61077 Kharkov, Ukraine
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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