Structure of the Lipschitz free p-spaces Fp(Zd) and Fp(Rd) for 0 < p≤ 1

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F22%3A00560291" target="_blank" >RIV/67985840:_____/22:00560291 - isvavai.cz</a>
Alternative codes found
RIV/00216208:11320/22:10456414
Result on the web
<a href="https://doi.org/10.1007/s13348-021-00322-9" target="_blank" >https://doi.org/10.1007/s13348-021-00322-9</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/s13348-021-00322-9" target="_blank" >10.1007/s13348-021-00322-9</a>

Result language
angličtina
Original language name
Structure of the Lipschitz free p-spaces Fp(Zd) and Fp(Rd) for 0 < p≤ 1
Original language description
Our aim in this article is to contribute to the theory of Lipschitz free p-spaces for 0 < p≤ 1 over the Euclidean spaces Rd and Zd. To that end, we show that Fp(Rd) admits a Schauder basis for every p∈ (0 , 1] , thus generalizing the corresponding result for the case p= 1 by Hájek and Pernecká (J Math Anal Appl 416(2):629–646, 2014, Theorem 3.1) and answering in the positive a question that was raised by Albiac et al. in (J Funct Anal 278(4):108354, 2020). Explicit formulas for the bases of Fp(Rd) and its isomorphic space Fp([0 , 1] d) are given. We also show that the well-known fact that F(Z) is isomorphic to ℓ1 does not extend to the case when p< 1 , that is, Fp(Z) is not isomorphic to ℓp when 0 < p< 1.
Czech name
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Czech description
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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

Project
<a href="/en/project/GX20-31529X" target="_blank" >GX20-31529X: Abstract convergence schemes and their complexities</a><br>
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2022
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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