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A forgotten theorem of Pełczyński: (λ+)-injective spaces need not be λ-injective—the case λ∈(1,2]

The result's identifiers

  • Result code in IS VaVaI

    <a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F23%3A00565258" target="_blank" >RIV/67985840:_____/23:00565258 - isvavai.cz</a>

  • Result on the web

    <a href="https://doi.org/10.4064/sm220119-25-6" target="_blank" >https://doi.org/10.4064/sm220119-25-6</a>

  • DOI - Digital Object Identifier

    <a href="http://dx.doi.org/10.4064/sm220119-25-6" target="_blank" >10.4064/sm220119-25-6</a>

Alternative languages

  • Result language

    angličtina

  • Original language name

    A forgotten theorem of Pełczyński: (λ+)-injective spaces need not be λ-injective—the case λ∈(1,2]

  • Original language description

    Isbell and Semadeni [Trans. Amer. Math. Soc. 107 (1963)] proved that every infinite-dimensional 1-injective Banach space contains a hyperplane that is (2+ epsilon)-injective for every epsilon > 0, yet is not 2-injective, and remarked in a footnote that Pelczynski had proved for every lambda > 1 the existence of a (lambda + epsilon)-injective space (epsilon > 0) that is not lambda-injective. Unfortunately, no trace of the proof of Pelczynski's result has been preserved. In the present paper, we establish that result for lambda is an element of (1, 2] by constructing an appropriate renorming of l(infinity). This contrasts (at least for real scalars) with the case lambda = 1 for which Lindenstrauss [Mem. Amer. Math. Soc. 48 (1964)] proved the contrary statement.

  • 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

  • Continuities

    I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Others

  • Publication year

    2023

  • Confidentiality

    S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Data specific for result type

  • Name of the periodical

    Studia mathematica

  • ISSN

    0039-3223

  • e-ISSN

    1730-6337

  • Volume of the periodical

    268

  • Issue of the periodical within the volume

    3

  • Country of publishing house

    PL - POLAND

  • Number of pages

    7

  • Pages from-to

    311-317

  • UT code for WoS article

    000859252400001

  • EID of the result in the Scopus database

    2-s2.0-85162894198