On the strongly subdifferentiable points in Lipschitz-free spaces

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21230%2F25%3A00389448" target="_blank" >RIV/68407700:21230/25:00389448 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.1007/s43037-024-00389-z" target="_blank" >https://doi.org/10.1007/s43037-024-00389-z</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/s43037-024-00389-z" target="_blank" >10.1007/s43037-024-00389-z</a>

Result language
angličtina
Original language name
On the strongly subdifferentiable points in Lipschitz-free spaces
Original language description
In this paper, we present some sufficient conditions on a metric space M for which every molecule is a strongly subdifferentiable (SSD, for short) point in the Lipschitz- free space F(M) over M. Our main result reads as follows: if (M , d) is a metric space and gamma > 0, then there exists a (not necessarily equivalent) metric d(gamma) in M such that every finitely supported element in F(M, d(gamma)) is an SSD point. As an application of the main result, it follows that if M is uniformly discrete and epsilon > 0 is given, there exists a metric space N and a (1 + e)-bi-Lipschitz map Phi : M -> N such that the set of all SSD points in F(N) is dense.
Czech name
—
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
—
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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