Operators affiliated to Banach lattice properties and their enveloping norms Full article
| Journal |
Turkish Journal of Mathematics
ISSN: 1300-0098 |
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| Output data | Year: 2023, Volume: 6, Number: 47, Article number : 5, Pages count : 15 DOI: 10.55730/1300-0098.3455 | ||||
| Tags | Banach lattice, affiliated operators, enveloping norm, domination problem | ||||
| Authors |
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| Affiliations |
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Funding (1)
| 1 | Sobolev Institute of Mathematics | FWNF-2022-0004 |
Abstract:
Several recent papers were devoted to various modifications of limited, Grothendieck, and Dunford-Pettis operators, etc., through involving the Banach lattice structure. In the present paper, it is shown that many of these operators appear as operators affiliated to well-known properties of Banach lattices, like the disjoint (dual) Schur property, the disjoint Grothendieck property, the property (d), the sequential w*-continuity of the lattice operations, etc. We also introduce new classes of operators such as the s-GPP-operators, s-BDP-operators, and bi-sP-operators. It is proved that the spaces consisting of regular versions of the above-mentioned operators are all the Banach spaces. The domination problem for these operators is investigated.
Cite:
Emelyanov E.
, Gorokhova S.
Operators affiliated to Banach lattice properties and their enveloping norms
Turkish Journal of Mathematics. 2023. V.6. N47. 5 :1-15. DOI: 10.55730/1300-0098.3455 WOS Scopus РИНЦ OpenAlex
Operators affiliated to Banach lattice properties and their enveloping norms
Turkish Journal of Mathematics. 2023. V.6. N47. 5 :1-15. DOI: 10.55730/1300-0098.3455 WOS Scopus РИНЦ OpenAlex
Dates:
| Submitted: | Jun 1, 2023 |
| Accepted: | Jul 5, 2023 |
| Published online: | Jul 5, 2023 |
| Published print: | Sep 25, 2023 |
Identifiers:
| Web of science: | WOS:001147340500008 |
| Scopus: | 2-s2.0-85172434785 |
| Elibrary: | 64556824 |
| OpenAlex: | W4387164391 |