Daugavet points and Δ-points in Lipschitz-free spaces

2020/10/19 by Jung, Mingu, Zoca, Abraham Rueda
#FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.2010.09357

Abstract

We study Daugavet points and Δ-points in Lipschitz-free Banach spaces. We prove that, if M is a compact metric space, then μ∈ S_{\mathcal F(M)} is a Daugavet point if, and only if, there is no denting point of B_{\mathcal F(M)} at distance strictly smaller than two from μ. Moreover, we prove that if x and y are connectable by rectifiable curves of lenght as close to d(x,y) as we wish, then the molecule m_x,y is a Δ-point. Some conditions on M which guarantee that the previous implication reverses are also obtained. As a consequence of our work, we show that Lipschitz-free spaces are natural examples of Banach spaces where we can guarantee the existence of Δ-points which are not Daugavet points.

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