Daugavet- and Delta-points in spaces of Lipschitz functions

2022/06/07 by Triinu Veeorg, Veeorg, Triinu · 1 citation
Mathematics · Computer Science · #Advanced Banach Space Theory #Optimization and Variational Analysis #Advanced Topology and Set Theory

paper · pdf · doi:10.48550/arxiv.2206.03475

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. We prove the equivalence of Daugavet- and Δ-points in spaces of Lipschitz functions over proper metric spaces and provide two characterizations for them. Furthermore, we show that in some spaces of Lipschitz functions, there exist Δ-points that are not Daugavet-points. Lastly, we prove that every space of Lipschitz functions over an infinite metric space contains a Δ-point but might not contain any Daugavet-points.

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