# Wydawnictwa / Czasopisma IMPAN / Bulletin Polish Acad. Sci. Math. / Wszystkie zeszyty

## Quotients of Banach Spaces with the Daugavet Property

### Tom 56 / 2008

Bulletin Polish Acad. Sci. Math. 56 (2008), 131-147 MSC: Primary 46B04; Secondary 46B03, 46B25, 47B38. DOI: 10.4064/ba56-2-5

#### Streszczenie

We consider a general concept of Daugavet property with respect to a norming subspace. This concept covers both the usual Daugavet property and its weak$^*$ analogue. We introduce and study analogues of narrow operators and rich subspaces in this general setting and apply the results to show that a quotient of $L_1[0,1]$ by an $\ell_1$-subspace need not have the Daugavet property. The latter answers in the negative a question posed to us by A. Pełczyński.

#### Autorzy

• Vladimir KadetsDepartment of Mechanics and Mathematics
Kharkov National University
pl. Svobody 4
61077 Kharkov, Ukraine
e-mail
• Varvara ShepelskaDepartment of Mechanics and Mathematics
Kharkov National University
pl. Svobody 4
61077 Kharkov, Ukraine
e-mail
• Dirk WernerDepartment of Mathematics
Freie Universität Berlin
Arnimallee 6
D-14195 Berlin, Germany
e-mail

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