Modulus of dentability in $L¹+L^{\infty }$

Adam Bohonos, and Ryszard Płuciennik. "Modulus of dentability in $L¹ + L^{∞}$." Banach Center Publications 79.1 (2008): 39-51. <http://eudml.org/doc/281846>.

@article{AdamBohonos2008,
abstract = {We introduce the notion of the modulus of dentability defined for any point of the unit sphere S(X) of a Banach space X. We calculate effectively this modulus for denting points of the unit ball of the classical interpolation space $L¹ + L^\{∞\}.$ Moreover, a criterion for denting points of the unit ball in this space is given. We also show that none of denting points of the unit ball of $L¹ + L^\{∞\}$ is a LUR-point. Consequently, the set of LUR-points of the unit ball of $L¹ + L^\{∞\}$ is empty.},
author = {Adam Bohonos, Ryszard Płuciennik},
journal = {Banach Center Publications},
keywords = {Köthe space; interpolation space; denting point; modulus of dentability; LUR-point},
language = {eng},
number = {1},
pages = {39-51},
title = {Modulus of dentability in $L¹ + L^\{∞\}$},
url = {http://eudml.org/doc/281846},
volume = {79},
year = {2008},
}

TY - JOUR
AU - Adam Bohonos
AU - Ryszard Płuciennik
TI - Modulus of dentability in $L¹ + L^{∞}$
JO - Banach Center Publications
PY - 2008
VL - 79
IS - 1
SP - 39
EP - 51
AB - We introduce the notion of the modulus of dentability defined for any point of the unit sphere S(X) of a Banach space X. We calculate effectively this modulus for denting points of the unit ball of the classical interpolation space $L¹ + L^{∞}.$ Moreover, a criterion for denting points of the unit ball in this space is given. We also show that none of denting points of the unit ball of $L¹ + L^{∞}$ is a LUR-point. Consequently, the set of LUR-points of the unit ball of $L¹ + L^{∞}$ is empty.
LA - eng
KW - Köthe space; interpolation space; denting point; modulus of dentability; LUR-point
UR - http://eudml.org/doc/281846
ER -