Isometries of Lipschitz-free Banach spaces

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F24%3A00600107" target="_blank" >RIV/67985840:_____/24:00600107 - isvavai.cz</a>
Alternative codes found
RIV/00216208:11320/24:10492947
Result on the web
<a href="https://doi.org/10.1112/jlms.70000" target="_blank" >https://doi.org/10.1112/jlms.70000</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1112/jlms.70000" target="_blank" >10.1112/jlms.70000</a>

Result language
angličtina
Original language name
Isometries of Lipschitz-free Banach spaces
Original language description
We describe surjective linear isometries and linear isometry groups of a large class of Lipschitz-free spaces that includes, for example, Lipschitz-free spaces over any graph. We define the notion of a Lipschitz-free rigid metric space whose Lipschitz-free space only admits surjective linear isometries coming from surjective dilations (i.e., rescaled isometries) of the metric space itself. We show that this class of metric spaces is surprisingly rich and contains all 3-connected graphs as well as geometric examples such as nonabelian Carnot groups with horizontally strictly convex norms. We prove that every metric space isometrically embeds into a Lipschitz-free rigid space that has only three more points.
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
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2024
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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