The Daugavet property for spaces of Lipschitz functions

2007/12/01 by Yevgen Ivakhno, Vladimir Kadets, Dirk Werner · 1 voice · 2 citations
Mathematics · Computer Science · #Advanced Banach Space Theory #Optimization and Variational Analysis #Advanced Topology and Set Theory

paper · pdf · doi:10.7146/math.scand.a-15044

openalex publication_date 2007/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/06/23

Abstract

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

Citations

• Banach spaces with the Daugavet property

Cited by

• The Daugavet property is equivalent to the polynomial Daugavet property
• A characterisation of the Daugavet property in spaces of Lipschitz\n functions

Discussions

• In general the answer is no and I do not know a characterization of when the answer is yes. There are finite dimensional counterexamples although the simplest counterexamples I have found are infinite [stackexchange, 1 points]

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