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Sibirskii Matematicheskii Zhurnal, 2016, Volume 57, Number 3, Pages 700–708
DOI: https://doi.org/10.17377/smzh.2016.57.319 (Mi smj2777) 		 
This article is cited in 22 scientific papers (total in 23 papers)

On extension of abstract Urysohn operators

M. A. Plieva, M. M. Popovbc

a Southern Mathematical Institute, Vladikavkaz Scientific Center of the Russian Academy of Sciences, Vladikavkaz, Russia
b Yuriy Fedkovych Chernivtsi National University, Chernivtsi, Ukraine
c Institute of Mathematics, Pomeranian University, Slupsk, Poland
Full-text PDF (437 kB) Citations (23)
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DOI: https://doi.org/10.17377/smzh.2016.57.319
Abstract: We consider the extension of an orthogonally additive operator from a lateral ideal and a lateral band to the whole space. We prove in particular that every orthogonally additive operator, extended from a lateral band of an order complete vector lattice, preserves lateral continuity, narrowness, compactness, and disjointness preservation. These results involve the strengthening of a recent theorem about narrow orthogonally additive operators in vector lattices.
Keywords: vector lattice, abstract Urysohn operator, lateral ideal, lateral band, smallest extension, laterally continuous operator, narrow operator.
Funding agency Grant number
Russian Foundation for Basic Research 15-51-53119
The first author was supported by the Russian Foundation for Basic Research (Grant 15-51-53119).
Received: 28.04.2015
Revised: 21.12.2015
English version:
Siberian Mathematical Journal, 2016, Volume 57, Issue 3, Pages 552–557
DOI: https://doi.org/10.1134/S0037446616030198
Bibliographic databases:
Document Type: Article
UDC: 517.98+519.46
Language: Russian
Citation: M. A. Pliev, M. M. Popov, “On extension of abstract Urysohn operators”, Sibirsk. Mat. Zh., 57:3 (2016), 700–708; Siberian Math. J., 57:3 (2016), 552–557
Citation in format AMSBIB
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    • This publication is cited in the following 23 articles:
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    		Сибирский математический журнал Siberian Mathematical Journal
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