The uniform boundedness principle for order bounded operators
Under appropriate hypotheses on the spaces, it is shown that a sequence of order bounded linear operators which is pointwise order bounded is uniformly order bounded on order bounded subsets. This result is used to establish a Banach-Steinhaus Theorem for order bounded operators.
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
1989-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/S0161171289000621 |
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| _version_ | 1832567309454016512 |
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| author | Charles Swartz |
| author_facet | Charles Swartz |
| author_sort | Charles Swartz |
| collection | DOAJ |
| description | Under appropriate hypotheses on the spaces, it is shown that a sequence
of order bounded linear operators which is pointwise order bounded is uniformly
order bounded on order bounded subsets. This result is used to establish a
Banach-Steinhaus Theorem for order bounded operators. |
| format | Article |
| id | doaj-art-5bd94f93f0fd4110a4126e601667ff38 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 1989-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-5bd94f93f0fd4110a4126e601667ff382025-02-03T01:01:45ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251989-01-0112348749210.1155/S0161171289000621The uniform boundedness principle for order bounded operatorsCharles Swartz0Department of Mathematical Sciences, New Mexico State University, Las Cruces 88003, NM, USAUnder appropriate hypotheses on the spaces, it is shown that a sequence of order bounded linear operators which is pointwise order bounded is uniformly order bounded on order bounded subsets. This result is used to establish a Banach-Steinhaus Theorem for order bounded operators.http://dx.doi.org/10.1155/S0161171289000621 |
| spellingShingle | Charles Swartz The uniform boundedness principle for order bounded operators International Journal of Mathematics and Mathematical Sciences |
| title | The uniform boundedness principle for order bounded operators |
| title_full | The uniform boundedness principle for order bounded operators |
| title_fullStr | The uniform boundedness principle for order bounded operators |
| title_full_unstemmed | The uniform boundedness principle for order bounded operators |
| title_short | The uniform boundedness principle for order bounded operators |
| title_sort | uniform boundedness principle for order bounded operators |
| url | http://dx.doi.org/10.1155/S0161171289000621 |
| work_keys_str_mv | AT charlesswartz theuniformboundednessprinciplefororderboundedoperators AT charlesswartz uniformboundednessprinciplefororderboundedoperators |