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Quotients of Banach spaces with the Daugavet property

Kadets V., Shepelska V., Werner D.

Bulletin of the Polish Academy of Sciences. Mathematics

2008

Vol. 56, no 2

131-147

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 L1[0,1] by an l1-subspace need not have the Daugavet property. The latter answers in the negative a question posed to us by A. Pełczyński.