A note on Delta-points in Lipschitz-free spaces

Abstract

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 that is almost at distance 2 from x. It is known that any finitely supported element μ in the unit sphere of a Lipschitz-free space ℱ (M) is a Δ-point if and only if for every ε > 0 and a slice S of B_ℱ(M) with μ ∈ S_ℱ(M) there exist u, v ∈ M with u ≠ v such that m_uv ∈ S and d(u,v) < ε. The aim of this note is to show that this characterization can also be applied to certain convex series of molecules.