Integral Representation and Supports of Functionals on Lipschitz Spaces

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21240%2F23%3A00371920" target="_blank" >RIV/68407700:21240/23:00371920 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.1093/imrn/rnab329" target="_blank" >https://doi.org/10.1093/imrn/rnab329</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1093/imrn/rnab329" target="_blank" >10.1093/imrn/rnab329</a>

Result language
angličtina
Original language name
Integral Representation and Supports of Functionals on Lipschitz Spaces
Original language description
We analyze the relationship between Borel measures and continuous linear functionals on the space Lip_0(M) of Lipschitz functions on a complete metric space M. In particular, we describe continuous functionals arising from measures and vice versa. In the case of weak* continuous functionals, that is, members of the Lipschitz-free space F(M), measures on M are considered. For the general case, we show that the appropriate setting is rather the uniform (or Samuel) compactification of M and that it is consistent with the treatment of F(M). This setting also allows us to give a definition of support for all elements of Lip_0(M)* with similar properties to those in F(M), and we show that it coincides with the support of the representing measure when such a measure exists. We deduce that the members of Lip_0(M)* that can be expressed as the difference of two positive functionals admit a Jordan-like decomposition into a positive and a negative part.
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
2023
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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