THE DAUGAVET PROPERTY FOR SPACES OF LIPSCHITZ FUNCTIONS

By Y. Ivakhno, V. Kadets, Dirk Werner. 2005

61 citations recorded by the source corpus.

For a compact metric space $K$ the space $\mathrm{Lip}(K)$ has the Daugavet property if and only if the norm of every $f \in \mathrm{Lip}(K)$ is attained locally. If $K$ is a subset of an $L_p$-space, $1<p<\infty$, this is equivalent to the convexity of $K$.

Subfields: Computational Theory and Mathematics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/e5e3122d33a6410987630e5101b0f823307ab1d9

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Citations in the corpus

• Extremal Structure and Duality of Lipschitz Free Spaces (2017, background): “The properties collected in the next lemma have already been proved in [17].”
• On strongly norm attaining Lipschitz maps (2018, background): “It is proved in [28] that, for a compact pointed metric space M , the space Lip0(M,R) has the Daugavet property if and only ifM has property (Z).”
• A characterisation of the Daugavet property in spaces of Lipschitz functions (2017, background): “(ii)⇒(iii) is trivial and (i)⇒(ii) was proved in [19], see the remark after Proposition 2.”