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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Sakarya University
2024-04-01
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| Series: | Sakarya Üniversitesi Fen Bilimleri Enstitüsü Dergisi |
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| Online Access: | https://dergipark.org.tr/tr/download/article-file/3456529 |
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| author | Gül Sinem Keleş Birol Altın |
| author_facet | Gül Sinem Keleş Birol Altın |
| author_sort | Gül Sinem Keleş |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-e7a7647ff8bd4ccdaddc9f12a7583aa2 |
| institution | Kabale University |
| issn | 2147-835X |
| language | English |
| publishDate | 2024-04-01 |
| publisher | Sakarya University |
| record_format | Article |
| series | Sakarya Üniversitesi Fen Bilimleri Enstitüsü Dergisi |
| spelling | doaj-art-e7a7647ff8bd4ccdaddc9f12a7583aa22024-12-23T08:17:25ZengSakarya UniversitySakarya Üniversitesi Fen Bilimleri Enstitüsü Dergisi2147-835X2024-04-0128236437010.16984/saufenbilder.137174428The Class of Demi-Strongly Order Bounded OperatorsGül Sinem Keleş0https://orcid.org/0000-0001-5712-239XBirol Altın1https://orcid.org/0000-0002-1085-809XGAZI UNIVERSITYGazı UniversityIn 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.https://dergipark.org.tr/tr/download/article-file/3456529riesz spacestrongly order bounded operatorb-propertypre-regular operator |
| spellingShingle | Gül Sinem Keleş Birol Altın The Class of Demi-Strongly Order Bounded Operators Sakarya Üniversitesi Fen Bilimleri Enstitüsü Dergisi riesz space strongly order bounded operator b-property pre-regular operator |
| title | The Class of Demi-Strongly Order Bounded Operators |
| title_full | The Class of Demi-Strongly Order Bounded Operators |
| title_fullStr | The Class of Demi-Strongly Order Bounded Operators |
| title_full_unstemmed | The Class of Demi-Strongly Order Bounded Operators |
| title_short | The Class of Demi-Strongly Order Bounded Operators |
| title_sort | class of demi strongly order bounded operators |
| topic | riesz space strongly order bounded operator b-property pre-regular operator |
| url | https://dergipark.org.tr/tr/download/article-file/3456529 |
| work_keys_str_mv | AT gulsinemkeles theclassofdemistronglyorderboundedoperators AT birolaltın theclassofdemistronglyorderboundedoperators AT gulsinemkeles classofdemistronglyorderboundedoperators AT birolaltın classofdemistronglyorderboundedoperators |