The Daugavet property in spaces of vector-valued Lipschitz functions

2022/02/14 by Abraham Rueda Zoca, Zoca, Abraham Rueda
Computer Science · Mathematics · #Advanced Banach Space Theory #Advanced Topology and Set Theory #FOS: Mathematics #Functional Analysis (math.FA) #Optimization and Variational Analysis

paper · pdf · doi:10.48550/arxiv.2202.06664

openalex publication_date 2022/02/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove that if a metric space M has the finite CEP then \mathcal F(M)\widehat⊗_π X has the Daugavet property for every non-zero Banach space X. This applies, for instance, if M is a Banach space whose dual is isometrically an L₁(μ) space. If M has the CEP then L(\mathcal F(M),X)=\Lip(M,X) has the Daugavet property for every non-zero Banach space X, showing that this is the case when M is an injective Banach space or a convex subset of a Hilbert space.

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