Modulus of dentability in $L^{1}+L^{\infty }$
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.
