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

Kód výsledku v 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>

Výsledek na webu

<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>

Jazyk výsledku

angličtina

Název v původním jazyce

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

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

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

Popis výsledku anglicky

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.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

—

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2023

Kód důvěrnosti údajů

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

Název periodika

Studia mathematica

ISSN

0039-3223

e-ISSN

1730-6337

Svazek periodika

268

Číslo periodika v rámci svazku

3

Stát vydavatele periodika

PL - Polská republika

Počet stran výsledku

7

Strana od-do

311-317

Kód UT WoS článku

000859252400001

EID výsledku v databázi Scopus

2-s2.0-85162894198