On the extension of one-parameter operator semigroups to completions of Archimedean vector lattices
Abstract
Extensions of one-parameter operator semigroups on Archimedean vector lattices to their completions and $\mathrm{(ru)}$-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 $\mathrm{(ru)}$-completions of vector lattices with property (R) is proved. It ensures the preservation of $\mathrm{(ru)}$-continuity and allows one to drop the assumption of the $\mathrm{(ru)}$-completeness of a lattice in many results on positive semigroups that are $\mathrm{(ru)}$-continuous at zero. Bibliography: 19 titles.
Fields of Study & Subjects
advanced mathematical theories
Publication details
- Journal / source
- Sbornik Mathematics
- Volume
- 217
- Issue
- 2
- Pages
- 190–196
- Publication date
- 1 January 2026
- Language
- EN