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arXiv · 2010.09357

Daugavet points and $Δ$-points in Lipschitz-free spaces

Mingu Jung·Abraham Rueda Zoca
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Abstract

We study Daugavet points and $Δ$-points in Lipschitz-free Banach spaces. We prove that, if $M$ is a compact metric space, then $μ\in S_{\mathcal F(M)}$ 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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Mingu Jung, Abraham Rueda Zoca. 2021-01-12. Daugavet points and $Δ$-points in Lipschitz-free spaces. https://arxiv.org/abs/2010.09357

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