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 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 is a LUR-point. Consequently, the set of LUR-points of the unit ball of is empty.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-bc79-0-2,
author = {Adam Bohonos and Ryszard P\l uciennik},
title = {Modulus of dentability in $L$^1$ + L^{$\infty$}$
},
journal = {Banach Center Publications},
volume = {83},
year = {2008},
pages = {39-51},
zbl = {1144.46014},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc79-0-2}
}
Adam Bohonos; Ryszard Płuciennik. Modulus of dentability in $L¹ + L^{∞}$
. Banach Center Publications, Tome 83 (2008) pp. 39-51. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc79-0-2/