Integral Representation and Supports of Functionals on Lipschitz Spaces

Kód výsledku v 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>

Výsledek na webu

<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>

Jazyk výsledku

angličtina

Název v původním jazyce

Integral Representation and Supports of Functionals on Lipschitz Spaces

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

Integral Representation and Supports of Functionals on Lipschitz Spaces

Popis výsledku anglicky

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.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

<a href="/cs/project/GJ18-00960Y" target="_blank" >GJ18-00960Y: Vybraná témata nelineární funkcionální analýzy a teorie aproximací</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2023

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

International Mathematics Research Notices

ISSN

1073-7928

e-ISSN

1687-0247

Svazek periodika

2023

Číslo periodika v rámci svazku

4

Stát vydavatele periodika

GB - Spojené království Velké Británie a Severního Irska

Počet stran výsledku

69

Strana od-do

3004-3072

Kód UT WoS článku

000789440400001

EID výsledku v databázi Scopus

2-s2.0-85152201636