On operators dominated by the Kantorovich-Banach and Levi operators in locally solid lattices. Full article
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Siberian Mathematical Journal
ISSN: 0037-4466 , E-ISSN: 1573-9260 |
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| Output data | Year: 2023, Volume: 64, Number: 3, Pages: 720-724 Pages count : 5 DOI: 10.1134/S0037446623030199 | ||||
| Tags | locally solid lattice, Lebesgue operator, Levi operator, KB-operator, lattice homomorphism | ||||
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| Affiliations |
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Funding (1)
| 1 | Sobolev Institute of Mathematics | FWNF-2022-0004 |
Abstract:
A linear operator T in a locally solid vector lattice (E,τ) is a Lebesgue operator, if Txα τ → 0 for every net in E satisfying xα ↓ 0; a KB-operator, if for every τ-bounded increasing net xα in E+ there exists x ∈ E with Txα τ → Tx; a quasi KB-operator, if T takes τ-bounded increasing nets in E+ to τ-Cauchy nets; a Levi operator, if for every τ-bounded increasing net xα in E+ there exists x ∈ E such that Txα o → Tx; and aquasi Levi operator, if T takes τ-bounded increasing nets in E+ to o-Cauchy ones. We address the domination problem for the quasi KB-operators and quasi Levi operators in locally solid vector lattices. Moreover, under study are some properties of Lebesgue, Levi, and KB-operators. In particular, we prove that the vector space of regularly Lebesgue operators is a subalgebra of the algebra of all regular operators.
Cite:
Gorokhova S.G.
, Emelyanov E.Y.
On operators dominated by the Kantorovich-Banach and Levi operators in locally solid lattices.
Siberian Mathematical Journal. 2023. V.64. N3. P.720-724. DOI: 10.1134/S0037446623030199 WOS Scopus РИНЦ OpenAlex
On operators dominated by the Kantorovich-Banach and Levi operators in locally solid lattices.
Siberian Mathematical Journal. 2023. V.64. N3. P.720-724. DOI: 10.1134/S0037446623030199 WOS Scopus РИНЦ OpenAlex
Original:
Горохова С.Г.
, Емельянов Э.Ю.
Об операторах, мажорируемых операторами Канторовича - Банаха и операторами Леви в локально солидных решетках
Владикавказский математический журнал (Vladikavkaz Mathematical Journal). 2022. Т.24. №3. С.55-61. DOI: 10.46698/f5525-0005-3031-h Scopus РИНЦ OpenAlex
Об операторах, мажорируемых операторами Канторовича - Банаха и операторами Леви в локально солидных решетках
Владикавказский математический журнал (Vladikavkaz Mathematical Journal). 2022. Т.24. №3. С.55-61. DOI: 10.46698/f5525-0005-3031-h Scopus РИНЦ OpenAlex
Dates:
| Submitted: | Oct 10, 2021 |
| Accepted: | Mar 4, 2023 |
| Published print: | May 24, 2023 |
| Published online: | May 24, 2023 |
Identifiers:
| Web of science: | WOS:000996393600019 |
| Scopus: | 2-s2.0-85160920068 |
| Elibrary: | 62466540 |
| OpenAlex: | W4377990865 |