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Sibirskii Matematicheskii Zhurnal, 2020, Volume 61, Number 2, Pages 330–336
DOI: https://doi.org/10.33048/smzh.2020.61.208 (Mi smj5985) 		 
This article is cited in 3 scientific papers (total in 3 papers)

Extension of positive operators

K. Yu. Il'inaa, Z. A. Kusraevabc

a North Ossetian State University after Kosta Levanovich Khetagurov, Vladikavkaz
b Regional mathematical center of Southern Federal University, Rostov-on-Don
c Southern Mathematical Institute of the Vladikavkaz Scientific Center of the Russian Academy of Sciences, Vladikavkaz
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DOI: https://doi.org/10.33048/smzh.2020.61.208
Abstract: The main result states that if $E$ is a separable Fréchet lattice and $F$ is a (locally solid) topological vector lattice with the $\sigma$-interpolation property then each positive linear operator $T_0$ from a majorizing subspace $G\subset E$ into $F$ admits extension to a continuous positive linear operator $T$ from $E$ into $F$. This fact is proved by using only the axiom of countable choice.
Keywords: topological vector lattice, Fréchet lattice, separability, $\sigma$-interpolation property, majorizing subspace, positive operator, axiom of countable choice.
Funding agency Grant number
Russian Foundation for Basic Research 18-31-00205
The authors were supported by the Russian Foundation for Basic Research (Grant 18-31-00205).</p><p>The authors are grateful to the referee for constructive remarks and comments.
Received: 04.06.2019
Revised: 29.10.2019
Accepted: 25.12.2019
English version:
Siberian Mathematical Journal, 2020, Volume 61, Issue 2, Pages 261–265
DOI: https://doi.org/10.1134/S0037446620020081
Bibliographic databases:
Document Type: Article
UDC: 517.98
MSC: 35R30
Language: Russian
Citation: K. Yu. Il'ina, Z. A. Kusraeva, “Extension of positive operators”, Sibirsk. Mat. Zh., 61:2 (2020), 330–336; Siberian Math. J., 61:2 (2020), 261–265
Citation in format AMSBIB
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    • This publication is cited in the following 3 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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