Quotients of Banach Spaces with the Daugavet Property
Bulletin of the Polish Academy of Sciences. Mathematics, Tome 56 (2008) no. 2, pp. 131-147
Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences
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.
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
Affiliations des auteurs :
Vladimir Kadets 1 ; Varvara Shepelska 1 ; Dirk Werner 2
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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},
pages = {131--147},
publisher = {mathdoc},
volume = {56},
number = {2},
year = {2008},
doi = {10.4064/ba56-2-5},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/ba56-2-5/}
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%0 Journal Article %A Vladimir Kadets %A Varvara Shepelska %A Dirk Werner %T Quotients of Banach Spaces with the Daugavet Property %J Bulletin of the Polish Academy of Sciences. Mathematics %D 2008 %P 131-147 %V 56 %N 2 %I mathdoc %U http://geodesic.mathdoc.fr/articles/10.4064/ba56-2-5/ %R 10.4064/ba56-2-5 %G en %F 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) no. 2, pp. 131-147. doi: 10.4064/ba56-2-5
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