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
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Czech description
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Classification
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
Result continuities
Project
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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