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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