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Pré-Publication, Document De Travail Année : 2017

A characterisation of the Daugavet property in spaces of Lipschitz functions

Luis García-Lirola
  • Fonction : Auteur
Abraham Rueda Zoca
  • Fonction : Auteur

Résumé

We study the Daugavet property in the space of Lipschitz functions $\operatorname{Lip}_0(M)$ for a complete metric space $M$. Namely we show that $\operatorname{Lip}_0(M)$ has the Daugavet property if and only if $M$ is a length space. This condition also characterises the Daugavet property in the Lipschitz free space $\mathcal{F}(M)$. Moreover, when $M$ is compact, we show that either $\mathcal{F}(M)$ has the Daugavet property or its unit ball has a strongly exposed point. If $M$ is an infinite compact subset of a strictly convex Banach space then the Daugavet property of $\operatorname{Lip}_0(M)$ is equivalent to the convexity of $M$.

Dates et versions

hal-01609314 , version 1 (03-10-2017)

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Citer

Luis García-Lirola, Antonin Prochazka, Abraham Rueda Zoca. A characterisation of the Daugavet property in spaces of Lipschitz functions. 2017. ⟨hal-01609314⟩
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