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The Daugavet property for spaces of Lipschitz functions

Yevgen Ivakhno·Vladimir Kadets·Dirk Werner
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Abstract

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

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Yevgen Ivakhno, Vladimir Kadets, Dirk Werner. 2005-09-16. The Daugavet property for spaces of Lipschitz functions. https://arxiv.org/abs/math/0509373

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