A note on the relationship between three classes of operators on Riesz spaces
Following several papers in the prior literature, we study the relationship between order bounded operators, topologically bounded operators and topologically continuous operators. Our main contribution is two-folded: (i) we provide a set of counterexamples to illustrate several extant results in th...
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| Format: | Article |
| Language: | English |
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Sciendo
2019-12-01
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| Series: | Annals of the West University of Timisoara: Mathematics and Computer Science |
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| Online Access: | https://doi.org/10.2478/awutm-2019-0016 |
| _version_ | 1818191917366640640 |
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| author | Hong Liang |
| author_facet | Hong Liang |
| author_sort | Hong Liang |
| collection | DOAJ |
| description | Following several papers in the prior literature, we study the relationship between order bounded operators, topologically bounded operators and topologically continuous operators. Our main contribution is two-folded: (i) we provide a set of counterexamples to illustrate several extant results in the literature; (ii) we give conditions for the space of order bounded operators to coincide with the space of topologically bounded operators as well as conditions for these two spaces to coincide with the space of topologically continuous operators. |
| first_indexed | 2024-12-12T00:22:13Z |
| format | Article |
| id | doaj.art-c806dcdf37b84d48a5ae750885561124 |
| institution | Directory Open Access Journal |
| issn | 1841-3307 |
| language | English |
| last_indexed | 2024-12-12T00:22:13Z |
| publishDate | 2019-12-01 |
| publisher | Sciendo |
| record_format | Article |
| series | Annals of the West University of Timisoara: Mathematics and Computer Science |
| spelling | doaj.art-c806dcdf37b84d48a5ae7508855611242022-12-22T00:44:42ZengSciendoAnnals of the West University of Timisoara: Mathematics and Computer Science1841-33072019-12-01572778510.2478/awutm-2019-0016A note on the relationship between three classes of operators on Riesz spacesHong Liang0John Jay 312, Department of Mathematics, Robert Morris University, 6001 University Blvd. Moon Township, PA 15108, USAFollowing several papers in the prior literature, we study the relationship between order bounded operators, topologically bounded operators and topologically continuous operators. Our main contribution is two-folded: (i) we provide a set of counterexamples to illustrate several extant results in the literature; (ii) we give conditions for the space of order bounded operators to coincide with the space of topologically bounded operators as well as conditions for these two spaces to coincide with the space of topologically continuous operators.https://doi.org/10.2478/awutm-2019-0016counterexampleslocally solid riesz spacesorder bounded operatorsregular operatorstopologically bounded operatorstopologically continuous operators |
| spellingShingle | Hong Liang A note on the relationship between three classes of operators on Riesz spaces Annals of the West University of Timisoara: Mathematics and Computer Science counterexamples locally solid riesz spaces order bounded operators regular operators topologically bounded operators topologically continuous operators |
| title | A note on the relationship between three classes of operators on Riesz spaces |
| title_full | A note on the relationship between three classes of operators on Riesz spaces |
| title_fullStr | A note on the relationship between three classes of operators on Riesz spaces |
| title_full_unstemmed | A note on the relationship between three classes of operators on Riesz spaces |
| title_short | A note on the relationship between three classes of operators on Riesz spaces |
| title_sort | note on the relationship between three classes of operators on riesz spaces |
| topic | counterexamples locally solid riesz spaces order bounded operators regular operators topologically bounded operators topologically continuous operators |
| url | https://doi.org/10.2478/awutm-2019-0016 |
| work_keys_str_mv | AT hongliang anoteontherelationshipbetweenthreeclassesofoperatorsonrieszspaces AT hongliang noteontherelationshipbetweenthreeclassesofoperatorsonrieszspaces |