On isometric embeddings into the set of strongly norm-attaining Lipschitz functions

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21230%2F23%3A00367884" target="_blank" >RIV/68407700:21230/23:00367884 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.1016/j.na.2023.113287" target="_blank" >https://doi.org/10.1016/j.na.2023.113287</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.na.2023.113287" target="_blank" >10.1016/j.na.2023.113287</a>

Result language
angličtina
Original language name
On isometric embeddings into the set of strongly norm-attaining Lipschitz functions
Original language description
In this paper, we provide an infinite metric space M such that the set SNA(M) of strongly norm-attaining Lipschitz functions on M does not contain a subspace which is linearly isometric to c0. This answers a question posed by Antonio Avilés, Gonzalo Martínez-Cervantes, Abraham Rueda Zoca, and Pedro Tradacete. On the other hand, we prove that SNA(M) contains an isometric copy of c0 whenever M is an infinite metric space which is not uniformly discrete. In particular, the latter holds true for all infinite compact metric spaces while it does not hold true for all proper metric spaces. We also provide some positive results in the non-separable setting.
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
Result was created during the realization of more than one project. More information in the Projects tab.
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2023
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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