Characterizations of Daugavet- and delta-points in Lipschitz-free spaces

Abstract

A norm one 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 almost at distance 2 from $x$. We characterize Daugavet- and $\Delta$-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.