Schauder bases in Lipschitz free spaces over nets in Banach spaces

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21230%2F22%3A00359469" target="_blank" >RIV/68407700:21230/22:00359469 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.1016/j.jmaa.2022.126178" target="_blank" >https://doi.org/10.1016/j.jmaa.2022.126178</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.jmaa.2022.126178" target="_blank" >10.1016/j.jmaa.2022.126178</a>

Result language
angličtina
Original language name
Schauder bases in Lipschitz free spaces over nets in Banach spaces
Original language description
In the present note we give two explicit constructions (based on a retractional argument) of a Schauder basis for the Lipschitz free space F(N), over certain uniformly discrete metric spaces N. The first one applies to every net N in a finite dimensional Banach space, leading to the basis constant independent of the dimension. The second one applies to grids in Banach spaces with an FDD. As a corollary, we obtain a retractional Schauder basis for the Lipschitz free space F(N) over a net N in every Banach space X with a Schauder basis containing a copy of c(0), as well as in every Banach space with a c(0)-like FDD. (C) 2022 Elsevier Inc. All rights reserved.
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/EF16_019%2F0000778" target="_blank" >EF16_019/0000778: Center for advanced applied science</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)<br>S - Specificky vyzkum na vysokych skolach

Publication year
2022
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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