A norm one element x of a Banach space is a Daugavet-point (respectively, a Δ-point) if every slice of the unit ball (respectively, every slice of the unit ball containing x) contains an element, which is almost at distance 2 from x. We characterize Daugavet- and Δ-points in Lipschitz-free spaces. Furthermore, we construct a Lipschitz-free space with the Radon--Nikod\'ym property and a Daugavet-point; this is the first known example of such a Banach space.
@article{arxiv.2111.14393,
title = {Characterizations of Daugavet- and delta-points in Lipschitz-free spaces},
author = {Triinu Veeorg},
journal= {arXiv preprint arXiv:2111.14393},
year = {2021}
}