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Sibirsk. Mat. Zh., 2017, Volume 58, Number 1, Pages 174–184 (Mi smj2850)  

This article is cited in 4 scientific papers (total in 4 papers)

Narrow orthogonally additive operators in lattice-normed spaces

M. A. Plievab, X. Fangc

a Southern Mathematical Institute, Vladikavkaz, Russia
b Peoples' Friendship University of Russia, Moscow, Russia
c Department of Mathematics, Tongji University, Shanghai, China

Abstract: We consider a new class of narrow orthogonally additive operators in lattice-normed spaces and prove the narrowness of every $C$-compact norm-laterally-continuous orthogonally additive operator from a Banach–Kantorovich space $V$ into a Banach space $Y$. Furthermore, every dominated Urysohn operator from $V$ into a Banach sequence lattice $Y$ is also narrow. We establish that the order narrowness of a dominated Urysohn operator from a Banach–Kantorovich space $V$ into a Banach space with mixed norm $W$ implies the order narrowness of the least dominant of the operator.

Keywords: vector lattice, Banach lattice, lattice-normed space, orthogonally additive operator, dominated Urysohn 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) and by the Ministry of Education and Science of the Russian Federation (Agreement 02.a03.21.0008 of 24 June 2016). The second author was supported by the National Natural Science Foundation of China (Grant 11511130012).


DOI: https://doi.org/10.17377/smzh.2017.58.117

Full text: PDF file (327 kB)
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English version:
Siberian Mathematical Journal, 2017, 58:1, 134–141

Bibliographic databases:

UDC: 517.98+519.46
MSC: 35R30
Received: 25.01.2016

Citation: M. A. Pliev, X. Fang, “Narrow orthogonally additive operators in lattice-normed spaces”, Sibirsk. Mat. Zh., 58:1 (2017), 174–184; Siberian Math. J., 58:1 (2017), 134–141

Citation in format AMSBIB
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\by M.~A.~Pliev, X.~Fang
\paper Narrow orthogonally additive operators in lattice-normed spaces
\jour Sibirsk. Mat. Zh.
\yr 2017
\vol 58
\issue 1
\pages 174--184
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\crossref{https://doi.org/10.17377/smzh.2017.58.117}
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\transl
\jour Siberian Math. J.
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\vol 58
\issue 1
\pages 134--141
\crossref{https://doi.org/10.1134/S0037446617010177}
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. N. M. Abasov, M. A. Pliev, “O summe uzkogo i $C$-kompaktnogo operatorov”, Vladikavk. matem. zhurn., 20:1 (2018), 3–9  mathnet  crossref
    2. N. Abasov, M. Pliev, “On two definitions of a narrow operator on Köthe-Bochner spaces”, Arch. Math., 111:2 (2018), 167–176  crossref  mathscinet  zmath  isi  scopus
    3. M. Pliev, K. Ramdane, “Order unbounded orthogonally additive operators in vector lattices”, Mediterr. J. Math., 15:2 (2018), 55  crossref  mathscinet  zmath  isi  scopus
    4. M. A. Pliev, M. R. Weber, “Finite elements in some vector lattices of nonlinear operators”, Positivity, 22:1 (2018), 245–260  crossref  mathscinet  zmath  isi  scopus
  • Сибирский математический журнал Siberian Mathematical Journal
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