Supports and extreme points in Lipschitz-free spaces

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21240%2F20%3A00341220" target="_blank" >RIV/68407700:21240/20:00341220 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.4171/RMI/1191" target="_blank" >https://doi.org/10.4171/RMI/1191</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.4171/RMI/1191" target="_blank" >10.4171/RMI/1191</a>

Result language
angličtina
Original language name
Supports and extreme points in Lipschitz-free spaces
Original language description
For a complete metric space M, we prove that the finitely supported extreme points of the unit ball of the Lipschitz-free space FM are precisely the elementary molecules (δ(p)-δ(q))/d(p,q) defined by pairs of points p,q in M such that the triangle inequality d(p,q)<d(p,r)+d(q,r) is strict for any relementM different from p and q. To this end, we show that the class of Lipschitz-free spaces over closed subsets of M is closed under arbitrary intersections when M has finite diameter, and that this allows a natural definition of the support of elements of FM.
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
—
OECD FORD branch
10101 - Pure mathematics

Project
<a href="/en/project/GJ18-00960Y" target="_blank" >GJ18-00960Y: Selected topics in non-linear functional analysis and approximation theory</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2020
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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