Convex integrals of molecules in Lipschitz-free spaces

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21240%2F24%3A00377295" target="_blank" >RIV/68407700:21240/24:00377295 - isvavai.cz</a>

Výsledek na webu

<a href="https://doi.org/10.1016/j.jfa.2024.110560" target="_blank" >https://doi.org/10.1016/j.jfa.2024.110560</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1016/j.jfa.2024.110560" target="_blank" >10.1016/j.jfa.2024.110560</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Convex integrals of molecules in Lipschitz-free spaces

Popis výsledku v původním jazyce

We introduce convex integrals of molecules in Lipschitz-free spaces F(M) as a continuous counterpart of convex series considered elsewhere, based on the de Leeuw representation. Using optimal transport theory, we show that these elements are determined by cyclical monotonicity of their supports, and that under certain finiteness conditions they agree with elements of F(M) that are induced by Radon measures on M, or that can be decomposed into positive and negative parts. We also show that convex integrals differ in general from convex series of molecules. Finally, we present some standalone results regarding extensions of Lipschitz functions which, combined with the above, yield applications to the extremal structure of F(M). In particular, we show that all elements of F(M) are convex series of molecules when M is uniformly discrete and identify all extreme points of the unit ball of F(M) in that case.

Název v anglickém jazyce

Convex integrals of molecules in Lipschitz-free spaces

Popis výsledku anglicky

We introduce convex integrals of molecules in Lipschitz-free spaces F(M) as a continuous counterpart of convex series considered elsewhere, based on the de Leeuw representation. Using optimal transport theory, we show that these elements are determined by cyclical monotonicity of their supports, and that under certain finiteness conditions they agree with elements of F(M) that are induced by Radon measures on M, or that can be decomposed into positive and negative parts. We also show that convex integrals differ in general from convex series of molecules. Finally, we present some standalone results regarding extensions of Lipschitz functions which, combined with the above, yield applications to the extremal structure of F(M). In particular, we show that all elements of F(M) are convex series of molecules when M is uniformly discrete and identify all extreme points of the unit ball of F(M) in that case.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

<a href="/cs/project/GA22-32829S" target="_blank" >GA22-32829S: Struktura volných Banachových prostorů a jejich druhých duálů</a><br>

Návaznosti

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

Rok uplatnění

2024

Kód důvěrnosti údajů

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

Název periodika

JOURNAL OF FUNCTIONAL ANALYSIS

ISSN

0022-1236

e-ISSN

1096-0783

Svazek periodika

287

Číslo periodika v rámci svazku

8

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

43

Strana od-do

—

Kód UT WoS článku

001268845100001

EID výsledku v databázi Scopus

2-s2.0-85198077144