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Sibirsk. Mat. Zh., 2014, Volume 55, Number 5, Pages 1118–1136 (Mi smj2592)  

This article is cited in 3 scientific papers (total in 3 papers)

On order bounded disjointness preserving operators

A. G. Kusraevab, S. S. Kutateladzec

a North Ossetian State University, Vladikavkaz, Russia
b Southern Mathematical Institute, Vladikavkaz Science Center of the Russian Academy of Sciences, Vladikavkaz, Russia
c Sobolev Institute of Mathematics, Novosibirsk, Russia

Abstract: The paper is aimed at demonstrating that some properties of order bounded operators in vector lattices are just Boolean valued interpretations of elementary properties of order bounded functionals. We present the general machinery and illustrate it with a few new results on order bounded disjointness preserving and $n$-disjoint operators.

Keywords: Boolean valued analysis, vector lattice, disjointness preserving operator, lattice homomorphism.

Full text: PDF file (411 kB)
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English version:
Siberian Mathematical Journal, 2014, 55:5, 915–928

Bibliographic databases:

UDC: 517.98
Received: 19.06.2014

Citation: A. G. Kusraev, S. S. Kutateladze, “On order bounded disjointness preserving operators”, Sibirsk. Mat. Zh., 55:5 (2014), 1118–1136; Siberian Math. J., 55:5 (2014), 915–928

Citation in format AMSBIB
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\by A.~G.~Kusraev, S.~S.~Kutateladze
\paper On order bounded disjointness preserving operators
\jour Sibirsk. Mat. Zh.
\yr 2014
\vol 55
\issue 5
\pages 1118--1136
\mathnet{http://mi.mathnet.ru/smj2592}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3289115}
\transl
\jour Siberian Math. J.
\yr 2014
\vol 55
\issue 5
\pages 915--928
\crossref{https://doi.org/10.1134/S0037446614050103}
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\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84911963901}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. A. G. Kusraev, S. S. Kutateladze, “A characterization of order bounded disjointness preserving bilinear operators”, Vladikavk. matem. zhurn., 17:1 (2015), 60–63  mathnet
    2. N. Abasov, M. Pliev, “Disjointness-preserving orthogonally additive operators in vector lattices”, Banach J. Math. Anal., 12:3 (2018), 730–750  crossref  mathscinet  zmath  isi  scopus
    3. K. H. Azar, R. Alavizadeh, “On the modulus of disjointness-preserving operators and $b$-$AM$-compact operators on Banach lattices”, Ann. Funct. Anal., 9:1 (2018), 101–110  crossref  mathscinet  zmath  isi  scopus
  • Сибирский математический журнал Siberian Mathematical Journal
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