On the extension of one-parameter operator semigroups to completions of Archimedean vector lattices Full article
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Sbornik Mathematics
ISSN: 1064-5616 , E-ISSN: 1468-4802 |
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| Output data | Year: 2026, Volume: 217, Number: 2, Pages: 190-196 Pages count : 7 DOI: 10.4213/sm10244e | ||
| Tags | one-parameter operator semigroup, convergence with a regulator, (ru)-continuity at zero, (ru)-completion, property (R). | ||
| Authors |
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| Affiliations |
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Funding (1)
| 1 | Министерство науки и высшего образования РФ | FWNF-2026-0022 |
Abstract:
Extensions of one-parameter operator semigroups on Archimedean vector lattices to their completions and (ru)-completions are studied. The existence and uniqueness of an extension is established in the class of positive semigroups. A theorem on the extension of positive semigroups to the (ru)-completions of vector lattices with property (R) is proved. It ensures the preservation of (ru)-continuity and allows one to drop the assumption of the (ru)-completeness of a lattice in many results on positive semigroups that are (ru)-continuous at zero.
Cite:
Emelyanov E.Y.
On the extension of one-parameter operator semigroups to completions of Archimedean vector lattices
Sbornik Mathematics. 2026. V.217. N2. P.190-196. DOI: 10.4213/sm10244e OpenAlex
On the extension of one-parameter operator semigroups to completions of Archimedean vector lattices
Sbornik Mathematics. 2026. V.217. N2. P.190-196. DOI: 10.4213/sm10244e OpenAlex
Original:
Emelyanov E.Y.
О продолжении однопараметрических операторных полугрупп на пополнения архимедовых векторных решеток
Математический сборник. 2026. Т.217. №2. С.71-78. DOI: 10.4213/sm10244 РИНЦ OpenAlex
О продолжении однопараметрических операторных полугрупп на пополнения архимедовых векторных решеток
Математический сборник. 2026. Т.217. №2. С.71-78. DOI: 10.4213/sm10244 РИНЦ OpenAlex
Dates:
| Submitted: | Dec 18, 2025 |
| Published online: | Apr 21, 2026 |
Identifiers:
| ≡ OpenAlex: | W4405767437 |