On the extension of one-parameter operator semigroups to completions of Archimedean vector lattices | Sciact - Система учета научной деятельности ИМ СО РАН

On the extension of one-parameter operator semigroups to completions of Archimedean vector lattices Научная публикация

Журнал

Sbornik Mathematics
ISSN: 1064-5616 , E-ISSN: 1468-4802

Вых. Данные

Год: 2026, Том: 217, Номер: 2, Страницы: 190-196 Страниц : 7 DOI: 10.4213/sm10244e

Ключевые слова

one-parameter operator semigroup, convergence with a regulator, (ru)-continuity at zero, (ru)-completion, property (R).

Авторы

Emelyanov Eduard Yur'evich ¹

Организации

1	Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk, Russia

Информация о финансировании (1)

Министерство науки и высшего образования РФ

FWNF-2026-0022

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.

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

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

Поступила в редакцию:	18 дек. 2025 г.
Опубликована online:	21 апр. 2026 г.

≡ OpenAlex:

W4405767437