Characterizations of Daugavet points and delta-points in Lipschitz-free spaces
Volume 268 / 2023
Studia Mathematica 268 (2023), 213-233
MSC: Primary 46B04; Secondary 46B20, 46B22.
DOI: 10.4064/sm220207-30-4
Published online: 8 August 2022
Abstract
A norm $1$ element $x$ of a Banach space is a Daugavet point (respectively, a $\Delta $-point) if every slice of the unit ball (respectively, every slice of the unit ball containing $x$) contains an element which is at distance almost 2 from $x$. We characterize Daugavet points and $\Delta $-points in Lipschitz-free spaces. Furthermore, we construct a Lipschitz-free space with the Radon–Nikodým property and with a Daugavet point; this is the first known example of such a Banach space.
