Lipschitz free spaces isomorphic to their infinite sums and geometric applications

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F21%3A00546797" target="_blank" >RIV/67985840:_____/21:00546797 - isvavai.cz</a>

Nalezeny alternativní kódy

RIV/00216208:11320/21:10441229

Výsledek na webu

<a href="https://doi.org/10.1090/tran/8444" target="_blank" >https://doi.org/10.1090/tran/8444</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1090/tran/8444" target="_blank" >10.1090/tran/8444</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Lipschitz free spaces isomorphic to their infinite sums and geometric applications

Popis výsledku v původním jazyce

We find general conditions under which Lipschitz-free spaces over metric spaces are isomorphic to their infinite direct _1-sum and exhibit several applications. As examples of such applications we have that Lipschitz-free spaces over balls and spheres of the same finite dimensions are isomorphic, that the Lipschitz-free space over Zd is isomorphic to its _1-sum, or that the Lipschitz-free space over any snowflake of a doubling metric space is isomorphic to l1. Moreover, following new ideas of Bruè et al. from [J. Funct. Anal. 280 (2021), pp. 108868, 21] we provide an elementary self-contained proof that Lipschitz-free spaces over doubling metric spaces are complemented in Lipschitz-free spaces over their superspaces and they have BAP. Everything, including the results about doubling metric spaces, is explored in the more comprehensive setting of p-Banach spaces, which allows us to appreciate the similarities and differences of the theory between the cases p < 1 and p = 1.

Název v anglickém jazyce

Lipschitz free spaces isomorphic to their infinite sums and geometric applications

Popis výsledku anglicky

We find general conditions under which Lipschitz-free spaces over metric spaces are isomorphic to their infinite direct _1-sum and exhibit several applications. As examples of such applications we have that Lipschitz-free spaces over balls and spheres of the same finite dimensions are isomorphic, that the Lipschitz-free space over Zd is isomorphic to its _1-sum, or that the Lipschitz-free space over any snowflake of a doubling metric space is isomorphic to l1. Moreover, following new ideas of Bruè et al. from [J. Funct. Anal. 280 (2021), pp. 108868, 21] we provide an elementary self-contained proof that Lipschitz-free spaces over doubling metric spaces are complemented in Lipschitz-free spaces over their superspaces and they have BAP. Everything, including the results about doubling metric spaces, is explored in the more comprehensive setting of p-Banach spaces, which allows us to appreciate the similarities and differences of the theory between the cases p < 1 and p = 1.

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

2021

Kód důvěrnosti údajů

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

Název periodika

American Mathematical Society. Transactions

ISSN

0002-9947

e-ISSN

1088-6850

Svazek periodika

374

Číslo periodika v rámci svazku

10

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

32

Strana od-do

7281-7312

Kód UT WoS článku

000699713900017

EID výsledku v databázi Scopus

2-s2.0-85110910225