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d-Operators in Banach Lattices Full article

Journal Siberian Mathematical Journal
ISSN: 0037-4466 , E-ISSN: 1573-9260
Output data Year: 2025, Volume: 66, Number: 6, Pages: 1499 - 1508 Pages count : 10 DOI: 10.1134/S003744662506014X
Tags Banach lattice, disjoint bounded set, compact set, limited set, domination problem
Authors Emelyanov E.Yu. 1 , Erkurşun-Özcan N. 2 , Gorokhova S.G. 3
Affiliations
1 Sobolev Institute of Mathematics, Novosibirsk, Russia
2 Department of Mathematics, Faculty of Science, Hacettepe University, Ankara, Turkey
3 Southern Mathematical Institute, Vladikavkaz, Russia

Funding (1)

1 Sobolev Institute of Mathematics FWNF-2022-0004

Abstract: We study operators that carry disjoint bounded subsets of a Banach lattice into compact, weakly compact, and limited subsets of a Banach space. Surprisingly, these operators behave differently from classical compact, weakly compact, and limited operators. Examples demonstrating that these operators differ from the corresponding classical operators are presented. We introduce and study d-Andrews operators, which carry disjoint bounded sets into Dunford–Pettis sets. The domination problem and norm completeness are discussed for the above-mentioned operators. It is shown that, in general, the domination problem for d-limited operators has a negative solution. Natural conditions on the range are provided that yield positive solutions to the domination problem for d-limited and d-Andrews operators. It is shown that the linear spans of d-compact and d-weakly compact positive operators are complete with respect to their enveloping norms. The “almost versions” are also investigated.
Cite: Emelyanov E.Y. , Erkurşun-Özcan N. , Gorokhova S.G.
d-Operators in Banach Lattices
Siberian Mathematical Journal. 2025. V.66. N6. P.1499 - 1508. DOI: 10.1134/S003744662506014X WOS Scopus РИНЦ OpenAlex
Dates:
Submitted: Jul 15, 2025
Accepted: Sep 23, 2025
Published print: Nov 24, 2025
Published online: Nov 24, 2025
Identifiers:
Web of science: WOS:001622319900015
Scopus: 2-s2.0-105022638737
Elibrary: 84013607
OpenAlex: W7106517459
Citing: Пока нет цитирований
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