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 |
|
||||||
| Affiliations |
|
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
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