Collective Order Boundedness of Sets of Operators Between Ordered Vector Spaces
Abstract It is proved that: each collectively order continuous set of operators from an Archimedean ordered vector space with a generating cone to an ordered vector space is collectively order bounded; and each collectively order-to-norm bounded set of operators from an ordered Banach space with a closed generating cone to a normed space is norm bounded. Several applications to commutative operator semigroups on ordered vector spaces are given.
Authors
- Eduard Emelyanov (ORCID: https://orcid.org/0000-0002-8828-0398)
- Nazife Erkurşun-Özcan (ORCID: https://orcid.org/0000-0001-6301-9671)
- Svetlana Gorokhova (ORCID: https://orcid.org/0000-0001-7087-8140)
Institutions
- Sobolev Institute of Mathematics (RU)
- Vladikavkaz Institute of Management (RU)
- Federal State Budgetary Institution of Science Federal Scientific Center "Vladikavkaz Scientific Center of the Russian Academy of Sciences" (RU)
- Hacettepe University (TR)
Publication Details
- Journal
- Results in Mathematics
- Published
- 2025-03-15
- DOI
- https://doi.org/10.1007/s00025-025-02386-6
- Citations
- 1
- Primary Topic
- Advanced Banach Space Theory
- Type
- article
- Field-Weighted Citation Impact
- 3.69
Funders
- Hacettepe Üniversitesi
- Sobolev Institute of Mathematics, Siberian Branch, Russian Academy of Sciences