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

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Sibirskii Matematicheskii Zhurnal, 2017, Volume 58, Number 1, Pages 174–184
DOI: https://doi.org/10.17377/smzh.2017.58.117 (Mi smj2850)

This article is cited in 20 scientific papers (total in 20 papers)

Narrow orthogonally additive operators in lattice-normed spaces

M. A. Pliev^ab, X. Fang^c

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

Full-text PDF (327 kB) Citations (20)

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

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).

Received: 25.01.2016

English version:
Siberian Mathematical Journal, 2017, Volume 58, Issue 1, Pages 134–141
DOI: https://doi.org/10.1134/S0037446617010177

Bibliographic databases:

Document Type: Article

UDC: 517.98+519.46

MSC: 35R30

Language: Russian

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

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Linking options:

https://www.mathnet.ru/eng/smj2850

https://www.mathnet.ru/eng/smj/v58/i1/p174

This publication is cited in the following 20 articles:

Nonna Dzhusoeva, Eleonora Grishenko, Marat Pliev, Fedor Sukochev, “Narrow operators on C-complete lattice-normed spaces”, Nonlinear Analysis, 243 (2024), 113524
A. D. Arziev, K. K. Kudaybergenov, P. R. Oryinbaev, A. K. Tanirbergen, “Partial Integral Operators on Banach–Kantorovich Spaces”, Math. Notes, 114:1 (2023), 15–29
Marat Pliev, Fedor Sukochev, “Narrow operators on tensor products of Köthe spaces”, Journal of Mathematical Analysis and Applications, 522:1 (2023), 126950
Nazife Erkurşun-Özcan, Marat Pliev, “On orthogonally additive operators in C-complete vector lattices”, Banach J. Math. Anal., 16:1 (2022)
A. Gumenchuk, I. Krasikova, M. Popov, “On linear sections of orthogonally additive operators”, Mat. Stud., 58:1 (2022), 94
N. M. Abasov, “On band preserving orthogonally additive operators”, Sib. elektron. matem. izv., 18:1 (2021), 495–510
N. M. Abasov, “On a band generated by a disjointness preserving orthogonally additive operator”, Lobachevskii J. Math., 42:5, SI (2021), 851–856
M. Pliev, “On compact orthogonally additive operators”, Lobachevskii J. Math., 42:5, SI (2021), 989–995
M. Pliev, F. Sukochev, “The Kalton and Rosenthal type decomposition of operators in Köthe-Bochner spaces”, J. Math. Anal. Appl., 500:2 (2021), 125142
E. Basaeva, R. Kulaev, M. Pliev, “On orthogonally additive operators in Köthe-Bochner spaces”, Results Math., 76:1 (2021), 20
M. Pliev, “On C-compact orthogonally additive operators”, J. Math. Anal. Appl., 494:1 (2021), 124594
N. M. Abasov, “On the sum of narrow orthogonally additive operators”, Russian Math. (Iz. VUZ), 64:7 (2020), 1–6
R. Chill, M. Pliev, “Atomic operators in vector lattices”, Mediterr. J. Math., 17:5 (2020), 138
N. Abasov, “Completely additive and c-compact operators in lattice-normed spaces”, Ann. Funct. Anal., 11:4 (2020), 914–928
N. Abasov, M. Pliev, “Dominated orthogonally additive operators in lattice-normed spaces”, Adv. Oper. Theory, 4:1 (2019), 251–264
M. Pliev, F. Polat, M. Weber, “Narrow and c-compact orthogonally additive operators in lattice-normed spaces”, Results Math., 74:4 (2019), UNSP 157
N. M. Abasov, M. A. Pliev, “O summe uzkogo i $C$-kompaktnogo operatorov”, Vladikavk. matem. zhurn., 20:1 (2018), 3–9
N. Abasov, M. Pliev, “On two definitions of a narrow operator on Köthe-Bochner spaces”, Arch. Math., 111:2 (2018), 167–176
M. Pliev, K. Ramdane, “Order unbounded orthogonally additive operators in vector lattices”, Mediterr. J. Math., 15:2 (2018), 55
M. A. Pliev, M. R. Weber, “Finite elements in some vector lattices of nonlinear operators”, Positivity, 22:1 (2018), 245–260

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

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