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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-ba56-2-5,
author = {Vladimir Kadets and Varvara Shepelska and Dirk Werner},
title = {Quotients of Banach Spaces with the Daugavet Property},
journal = {Bulletin of the Polish Academy of Sciences. Mathematics},
volume = {56},
year = {2008},
pages = {131-147},
zbl = {1163.46005},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ba56-2-5}
}
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) pp. 131-147. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ba56-2-5/