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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

  • 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

    <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