Continuous operators from spaces of Lipschitz functions
The result's identifiers
Result code in 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>
Result on the web
<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>
Alternative languages
Result language
angličtina
Original language name
Continuous operators from spaces of Lipschitz functions
Original language description
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.
Czech name
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Czech description
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Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10101 - Pure mathematics
Result continuities
Project
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Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2025
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Results in Mathematics
ISSN
1422-6383
e-ISSN
1420-9012
Volume of the periodical
80
Issue of the periodical within the volume
1
Country of publishing house
DE - GERMANY
Number of pages
39
Pages from-to
5
UT code for WoS article
001375759800001
EID of the result in the Scopus database
2-s2.0-85211389328