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- Title
The Class of Demi-Strongly Order Bounded Operators.
- Authors
Keleş, Gül Sinem; Altın, Birol
- Abstract
In this paper, we introduce the class of demi-strongly order bounded operators on a Riesz space generalization of strongly order bounded operators. Let M be a Riesz space, an operator H from M into M is said to be a demi-strongly order bounded operator if for every net {uα} in M+ whenever 0 ≤ uα ↑ ≤ u ′′, u ′′ in M∼∼ and {uα −H(uα)} is order bounded in M, then {uα} is order bounded in M. We obtain a characterization of the b-property by the term of demi-strongly order bounded operators. In addition, we study the relationship between strongly order bounded operators and demi-strongly order bounded operators. Finally, we also investigate some properties of the class of demi-strongly order bounded operators.
- Subjects
RIESZ spaces; GENERALIZATION
- Publication
Sakarya University Journal of Science (SAUJS) / Sakarya Üniversitesi Fen Bilimleri Enstitüsü Dergisi, 2024, Vol 28, Issue 2, p364
- ISSN
1301-4048
- Publication type
Article
- DOI
10.16984/saufenbilder.1371744