Continuous operators from spaces of Lipschitz functions

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F25%3A00603076" target="_blank" >RIV/67985840:_____/25:00603076 - isvavai.cz</a>

Výsledek na webu

<a href="https://doi.org/10.1007/s00025-024-02323-z" target="_blank" >https://doi.org/10.1007/s00025-024-02323-z</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1007/s00025-024-02323-z" target="_blank" >10.1007/s00025-024-02323-z</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Continuous operators from spaces of Lipschitz functions

Popis výsledku v původním jazyce

We study the existence of continuous (linear) operators from the Banach spaces Lip0(M) of Lipschitz functions on infinite metric spaces M vanishing at a distinguished point and from their predual spaces F(M) onto certain Banach spaces, including C(K)-spaces and the spaces c0 and ℓ1. For pairs of spaces Lip0(M) and C(K) we prove that if they are endowed with topologies weaker than the norm topology, then usually no continuous (linear or not) surjection exists between those spaces. It is also showed that if a metric space M contains a bilipschitz copy of the unit sphere Sc0 of the space c0, then Lip0(M) admits a continuous operator onto ℓ1 and hence onto c0. Using this, we provide several conditions for a space M implying that Lip0(M) is not a Grothendieck space. Finally, we obtain a new characterization of the Schur property for Lipschitz-free spaces: a space F(M) has the Schur property if and only if for every complete discrete metric space N with cardinality d(M) the spaces F(M) and F(N) are weakly sequentially homeomorphic.

Název v anglickém jazyce

Continuous operators from spaces of Lipschitz functions

Popis výsledku anglicky

We study the existence of continuous (linear) operators from the Banach spaces Lip0(M) of Lipschitz functions on infinite metric spaces M vanishing at a distinguished point and from their predual spaces F(M) onto certain Banach spaces, including C(K)-spaces and the spaces c0 and ℓ1. For pairs of spaces Lip0(M) and C(K) we prove that if they are endowed with topologies weaker than the norm topology, then usually no continuous (linear or not) surjection exists between those spaces. It is also showed that if a metric space M contains a bilipschitz copy of the unit sphere Sc0 of the space c0, then Lip0(M) admits a continuous operator onto ℓ1 and hence onto c0. Using this, we provide several conditions for a space M implying that Lip0(M) is not a Grothendieck space. Finally, we obtain a new characterization of the Schur property for Lipschitz-free spaces: a space F(M) has the Schur property if and only if for every complete discrete metric space N with cardinality d(M) the spaces F(M) and F(N) are weakly sequentially homeomorphic.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

—

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2025

Kód důvěrnosti údajů

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

Název periodika

Results in Mathematics

ISSN

1422-6383

e-ISSN

1420-9012

Svazek periodika

80

Číslo periodika v rámci svazku

1

Stát vydavatele periodika

DE - Spolková republika Německo

Počet stran výsledku

39

Strana od-do

5

Kód UT WoS článku

001375759800001

EID výsledku v databázi Scopus

2-s2.0-85211389328