On Projectional Skeletons and the Plichko Property in Lipschitz-Free Banach Spaces

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21230%2F23%3A00370641" target="_blank" >RIV/68407700:21230/23:00370641 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.1007/s00009-023-02505-z" target="_blank" >https://doi.org/10.1007/s00009-023-02505-z</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/s00009-023-02505-z" target="_blank" >10.1007/s00009-023-02505-z</a>

Result language
angličtina
Original language name
On Projectional Skeletons and the Plichko Property in Lipschitz-Free Banach Spaces
Original language description
We study projectional skeletons and the Plichko property in Lipschitz-free spaces, relating these concepts to the geometry of the underlying metric space. Specifically, we identify a metric property that characterizes the Plichko property witnessed by Dirac measures in the associated Lipschitz-free space. We also show that the Lipschitz-free space of all R-trees has the Plichko property witnessed by molecules and define the concept of retractional trees to generalize this result to a bigger class of metric spaces. Finally, we show that no separable subspace of l(infinity) containing c0 is an r-Lipschitz retract for r < 2, which implies in particular that F(l(infinity)) is not r-Plichko for r < 2.
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
2023
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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