Projections in Lipschitz-free spaces induced by group actions

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F23%3A00575127" target="_blank" >RIV/67985840:_____/23:00575127 - isvavai.cz</a>

Nalezeny alternativní kódy

RIV/00216208:11320/23:10475536

Výsledek na webu

<a href="https://doi.org/10.1002/mana.202100222" target="_blank" >https://doi.org/10.1002/mana.202100222</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1002/mana.202100222" target="_blank" >10.1002/mana.202100222</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Projections in Lipschitz-free spaces induced by group actions

Popis výsledku v původním jazyce

We show that given a compact group G acting continuously on a metric space (Figure presented.) by bi-Lipschitz bijections with uniformly bounded norms, the Lipschitz-free space over the space of orbits (Figure presented.) (endowed with Hausdorff distance) is complemented in the Lipschitz-free space over (Figure presented.). We also investigate the more general case when G is amenable, locally compact or SIN and its action has bounded orbits. Then, we get that the space of Lipschitz functions (Figure presented.) is complemented in (Figure presented.). Moreover, if the Lipschitz-free space over (Figure presented.), (Figure presented.), is complemented in its bidual, several sufficient conditions on when (Figure presented.) is complemented in (Figure presented.) are given. Some applications are discussed. The paper contains preliminaries on projections induced by actions of amenable groups on general Banach spaces.

Název v anglickém jazyce

Projections in Lipschitz-free spaces induced by group actions

Popis výsledku anglicky

We show that given a compact group G acting continuously on a metric space (Figure presented.) by bi-Lipschitz bijections with uniformly bounded norms, the Lipschitz-free space over the space of orbits (Figure presented.) (endowed with Hausdorff distance) is complemented in the Lipschitz-free space over (Figure presented.). We also investigate the more general case when G is amenable, locally compact or SIN and its action has bounded orbits. Then, we get that the space of Lipschitz functions (Figure presented.) is complemented in (Figure presented.). Moreover, if the Lipschitz-free space over (Figure presented.), (Figure presented.), is complemented in its bidual, several sufficient conditions on when (Figure presented.) is complemented in (Figure presented.) are given. Some applications are discussed. The paper contains preliminaries on projections induced by actions of amenable groups on general Banach spaces.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

<a href="/cs/project/GJ19-05271Y" target="_blank" >GJ19-05271Y: Grupy a jejich akce, operátorové algebry a deskriptivní teorie množin</a><br>

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2023

Kód důvěrnosti údajů

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

Název periodika

Mathematische Nachrichten

ISSN

0025-584X

e-ISSN

1522-2616

Svazek periodika

296

Číslo periodika v rámci svazku

8

Stát vydavatele periodika

DE - Spolková republika Německo

Počet stran výsledku

17

Strana od-do

3301-3317

Kód UT WoS článku

000977802500001

EID výsledku v databázi Scopus

2-s2.0-85158073259