Quotients of Banach Spaces with the Daugavet Property

Vladimir Kadets, Varvara Shepelska, and Dirk Werner. "Quotients of Banach Spaces with the Daugavet Property." Bulletin of the Polish Academy of Sciences. Mathematics 56.2 (2008): 131-147. <http://eudml.org/doc/286584>.

@article{VladimirKadets2008,
abstract = {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.},
author = {Vladimir Kadets, Varvara Shepelska, Dirk Werner},
journal = {Bulletin of the Polish Academy of Sciences. Mathematics},
keywords = {Daugavet property; narrow operator; poor subspace; quotient space; Radon-Nikodým property; reflexive subspace; rich subspace},
language = {eng},
number = {2},
pages = {131-147},
title = {Quotients of Banach Spaces with the Daugavet Property},
url = {http://eudml.org/doc/286584},
volume = {56},
year = {2008},
}

TY - JOUR
AU - Vladimir Kadets
AU - Varvara Shepelska
AU - Dirk Werner
TI - Quotients of Banach Spaces with the Daugavet Property
JO - Bulletin of the Polish Academy of Sciences. Mathematics
PY - 2008
VL - 56
IS - 2
SP - 131
EP - 147
AB - 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.
LA - eng
KW - Daugavet property; narrow operator; poor subspace; quotient space; Radon-Nikodým property; reflexive subspace; rich subspace
UR - http://eudml.org/doc/286584
ER -