Supports in Lipschitz-free spaces and applications to extremal structure

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21240%2F20%3A00341057" target="_blank" >RIV/68407700:21240/20:00341057 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.1016/j.jmaa.2020.124128" target="_blank" >https://doi.org/10.1016/j.jmaa.2020.124128</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.jmaa.2020.124128" target="_blank" >10.1016/j.jmaa.2020.124128</a>

Result language
angličtina
Original language name
Supports in Lipschitz-free spaces and applications to extremal structure
Original language description
We show that the class of Lipschitz-free spaces over closed subsets of any complete metric space M is closed under arbitrary intersections, improving upon the previously known finite-diameter case. This allows us to formulate a general and natural definition of supports for elements in a Lipschitz-free space F(M). We then use this concept to study the extremal structure of F(M). We prove in particular that (δ(x) -δ(y))/d(x, y) is an exposed point of the unit ball of F(M) whenever the metric segment [x, y] is trivial, and that any extreme point which can be expressed as a finitely supported perturbation of a positive element must be finitely supported itself. We also characterize the extreme points of the positive unit ball: they are precisely the normalized evaluation functionals on points of M.
Czech name
—
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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