Lipschitz free spaces isomorphic to their infinite sums and geometric applications
The result's identifiers
Result code in 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>
Alternative codes found
RIV/00216208:11320/21:10441229
Result on the web
<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>
Alternative languages
Result language
angličtina
Original language name
Lipschitz free spaces isomorphic to their infinite sums and geometric applications
Original language description
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.
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
—
OECD FORD branch
10101 - Pure mathematics
Result continuities
Project
<a href="/en/project/GJ19-05271Y" target="_blank" >GJ19-05271Y: Groups and their actions, operator algebras, and descriptive set theory</a><br>
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2021
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
American Mathematical Society. Transactions
ISSN
0002-9947
e-ISSN
1088-6850
Volume of the periodical
374
Issue of the periodical within the volume
10
Country of publishing house
US - UNITED STATES
Number of pages
32
Pages from-to
7281-7312
UT code for WoS article
000699713900017
EID of the result in the Scopus database
2-s2.0-85110910225