A characterisation of the Daugavet property in spaces of vector-valued Lipschitz functions

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21230%2F25%3A00390245" target="_blank" >RIV/68407700:21230/25:00390245 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.1016/j.jfa.2025.110896" target="_blank" >https://doi.org/10.1016/j.jfa.2025.110896</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.jfa.2025.110896" target="_blank" >10.1016/j.jfa.2025.110896</a>

Result language
angličtina
Original language name
A characterisation of the Daugavet property in spaces of vector-valued Lipschitz functions
Original language description
Let M be a metric space and X be a Banach space. In this paper we address several questions about the structure of T(M)circle times pi X and Lip0(M, X). Our results are the following: (1) We prove that if M is a length metric space then Lip0(M, X) has the Daugavet property. As a consequence, if M is length we obtain that T(M)circle times pi X has the Daugavet property. This gives an affirmative answer to [9, Question 1] (also asked in [16, Remark 3.8]). (2) We prove that if M is a non-uniformly discrete metric space or an unbounded metric space then the norm of T(M)circle times pi X is octahedral, which solves [4, Question 3.2 (1)]. (3) We characterise all the Banach spaces X such that L(X, Y ) is octahedral for every Banach space Y, which solves a question by Johann Langemets. (c) 2025 Elsevier Inc. All rights are reserved, including those for text and data mining, AI training, and similar technologies.
Czech name
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Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10101 - Pure mathematics

Project
<a href="/en/project/GA23-04776S" target="_blank" >GA23-04776S: Interplay of algebraic, metric, geometric and topological structures on Banach spaces</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2025
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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