Embeddability of ℓp and bases in Lipschitz free p-spaces for 0 < p ≤ 1
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F20%3A00518256" target="_blank" >RIV/67985840:_____/20:00518256 - isvavai.cz</a>
Alternative codes found
RIV/00216208:11320/20:10422026
Result on the web
<a href="https://doi.org/10.1016/j.jfa.2019.108354" target="_blank" >https://doi.org/10.1016/j.jfa.2019.108354</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.jfa.2019.108354" target="_blank" >10.1016/j.jfa.2019.108354</a>
Alternative languages
Result language
angličtina
Original language name
Embeddability of ℓp and bases in Lipschitz free p-spaces for 0 < p ≤ 1
Original language description
Our goal in this paper is to continue the study initiated by the authors in [4] of the geometry of the Lipschitz free p-spaces over quasimetric spaces for 0<p≤1, denoted Fp(M). Here we develop new techniques to show that, by analogy with the case p=1, the space ℓp embeds isomorphically in Fp(M) for 0<p<1. Going further we see that despite the fact that, unlike the case p=1, this embedding need not be complemented in general, complementability of ℓp in a Lipschitz free p-space can still be attained by imposing certain natural restrictions to M. As a by-product of our discussion on bases in Fp([0,1]), we obtain examples of p-Banach spaces for p<1 that are not based on a trivial modification of Banach spaces, which possess a basis but fail to have an unconditional basis.
Czech name
—
Czech description
—
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
Result was created during the realization of more than one project. More information in the Projects tab.
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2020
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Journal of Functional Analysis
ISSN
0022-1236
e-ISSN
—
Volume of the periodical
278
Issue of the periodical within the volume
4
Country of publishing house
US - UNITED STATES
Number of pages
33
Pages from-to
108354
UT code for WoS article
000507143300005
EID of the result in the Scopus database
2-s2.0-85073926170