Modulus of dentability in
Volume 79 / 2008
Banach Center Publications 79 (2008), 39-51
MSC: 46E30, 46B20, 46B42.
DOI: 10.4064/bc79-0-2
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 L^{1}+L^{\infty }. 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 L^{1}+L^{\infty } is a LUR-point. Consequently, the set of LUR-points of the unit ball of L^{1}+L^{\infty } is empty.
