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Matematicheskie Zametki, 2023, Volume 113, Issue 1, Pages 58–74
DOI: https://doi.org/10.4213/mzm13613 (Mi mzm13613) 		 
This article is cited in 5 scientific papers (total in 5 papers)

On Orthogonally Additive Operators in Lattice-Normed Spaces

N. A. Dzhusoeva, S. Yu. Itarova

North Ossetian State University after Kosta Levanovich Khetagurov, Vladikavkaz
Full-text PDF (547 kB) Citations (5)
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DOI: https://doi.org/10.4213/mzm13613
Abstract: In this paper, we study a new class of locally dominated orthogonally additive operators on lattice-normed spaces (LNS). In the first part of the paper, sufficient conditions for the existence of a local exact majorant of a locally dominated operator and formulas for its calculation are given. The second part shows that the $C$-compactness of a dominated orthogonally additive operator acting from a decomposable lattice-normed space to a Banach space with mixed norm implies the $C$-compactness of its exact majorant.
Keywords: orthogonally additive operator, $x$-locally dominated operator, $x$-local exact majorant, positive operator, $C$-compact operator, lattice-normed space, vector lattice, Banach lattice.
Funding agency Grant number
Ministry of Science and Higher Education of the Russian Federation 075-02-2021-1552
This work was financially supported by the Ministry of Science and Higher Education of the Russian Federation, agreement no. 075-02-2021-1552.
Received: 05.06.2022
Revised: 06.08.2022
English version:
Mathematical Notes, 2023, Volume 113, Issue 1, Pages 59–71
DOI: https://doi.org/10.1134/S0001434623010078
Bibliographic databases:
Document Type: Article
UDC: 517
Language: Russian
Citation: N. A. Dzhusoeva, S. Yu. Itarova, “On Orthogonally Additive Operators in Lattice-Normed Spaces”, Mat. Zametki, 113:1 (2023), 58–74; Math. Notes, 113:1 (2023), 59–71
Citation in format AMSBIB
\Bibitem{DzhIta23}
\by N.~A.~Dzhusoeva, S.~Yu.~Itarova
\paper On Orthogonally Additive Operators in Lattice-Normed Spaces
\jour Mat. Zametki
\yr 2023
\vol 113
\issue 1
\pages 58--74
\mathnet{http://mi.mathnet.ru/mzm13613}
\crossref{https://doi.org/10.4213/mzm13613}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=4563349}
\transl
\jour Math. Notes
\yr 2023
\vol 113
\issue 1
\pages 59--71
\crossref{https://doi.org/10.1134/S0001434623010078}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85149937272}
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    • This publication is cited in the following 5 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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