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

Kód výsledku v 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>

Výsledek na webu

<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>

Jazyk výsledku

angličtina

Název v původním jazyce

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

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

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

Popis výsledku anglicky

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.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

<a href="/cs/project/GA23-04776S" target="_blank" >GA23-04776S: Interakce algebraických, metrických, geometrických a topologických struktur na Banachových prostorech</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2025

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

JOURNAL OF FUNCTIONAL ANALYSIS

ISSN

0022-1236

e-ISSN

1096-0783

Svazek periodika

289

Číslo periodika v rámci svazku

1

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

19

Strana od-do

—

Kód UT WoS článku

001442593600001

EID výsledku v databázi Scopus

2-s2.0-85219674896