Lipschitz retractions and complementation properties in Banach spaces

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21230%2F22%3A00359404" target="_blank" >RIV/68407700:21230/22:00359404 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.1016/j.jfa.2022.109494" target="_blank" >https://doi.org/10.1016/j.jfa.2022.109494</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.jfa.2022.109494" target="_blank" >10.1016/j.jfa.2022.109494</a>

Result language
angličtina
Original language name
Lipschitz retractions and complementation properties in Banach spaces
Original language description
In the present paper we introduce and study the Lipschitz retractional structure of metric spaces. This topic was motivated by the analogous projectional structure of Banach spaces, a topic that has been thoroughly investigated. The more general metric setting fits well with the currently active theory of Lipschitz free spaces and spaces of Lipschitz functions. Among our applications we show that the Lipschitz free space F (X) is a Plichko space whenever X is a Plichko Banach space. Our main results include two examples of metric spaces. The first one M contains two points {0, 1} such that no separable subset of M containing these points is a Lipschitz retract of M . The second example fails the analogous property for arbitrary infinite density. Finally, we introduce the metric version of the concept of locally complemented Banach subspace, and prove some metric analogues to the linear theory.
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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