Geodesic
Quotients of Banach Spaces with the Daugavet Property
Vladimir Kadets1 ; Varvara Shepelska1 ; Dirk Werner2
1Department of Mechanics and Mathematics Kharkov National University pl. Svobody 4 61077 Kharkov, Ukraine
2Department of Mathematics Freie Universität Berlin Arnimallee 6 D-14195 Berlin, Germany
Bulletin of the Polish Academy of Sciences. Mathematics, Tome 56 (2008) no. 2, pp. 131-147
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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.
DOI : 10.4064/ba56-2-5
Keywords: consider general concept daugavet property respect norming subspace concept covers usual daugavet property its weak * analogue introduce study analogues narrow operators rich subspaces general setting apply results quotient ell subspace have daugavet property latter answers negative question posed nbsp czy ski

Vladimir Kadets  1   ; Varvara Shepelska  1   ; Dirk Werner  2

1 Department of Mechanics and Mathematics Kharkov National University pl. Svobody 4 61077 Kharkov, Ukraine
2 Department of Mathematics Freie Universität Berlin Arnimallee 6 D-14195 Berlin, Germany 
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     title = {Quotients of {Banach} {Spaces} with the {Daugavet} {Property}},
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Vladimir Kadets; Varvara Shepelska; Dirk Werner. Quotients of Banach Spaces with the Daugavet Property. Bulletin of the Polish Academy of Sciences. Mathematics, Tome 56 (2008) no. 2, pp. 131-147. doi: 10.4064/ba56-2-5

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