The Class of Demi-Strongly Order Bounded Operators
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 {u_α} in M^+ whenever 0≤u_α↑ ≤...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Sakarya University
2024-04-01
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| Series: | Sakarya Üniversitesi Fen Bilimleri Enstitüsü Dergisi |
| Subjects: | |
| Online Access: | https://dergipark.org.tr/tr/download/article-file/3456529 |
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| Summary: | 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 {u_α} in M^+ whenever 0≤u_α↑ ≤u^'',u^'' in M^(∼∼) and {u_α-H(u_α )} is order bounded in M, then {u_α} 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. |
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| ISSN: | 2147-835X |