Collective order boundedness of sets of operators between ordered vector spaces
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866915133981196288 |
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| author | Emelyanov, Eduard Erkursun-Ozcan, Nazife Gorokhova, Svetlana |
| author_facet | Emelyanov, Eduard Erkursun-Ozcan, Nazife Gorokhova, Svetlana |
| contents | It is proved that: each collectively order continuous set of operators from an Archimedean OVS with a generating cone to an OVS is collectively order bounded; and each collectively order to norm bounded set of operators from an ordered Banach space with a closed generating cone to a normed space is norm bounded. Several applications to commutative operator semigroups on ordered vector spaces are given. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_17030 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Collective order boundedness of sets of operators between ordered vector spaces Emelyanov, Eduard Erkursun-Ozcan, Nazife Gorokhova, Svetlana Functional Analysis 46A40, 46B42, 47B60, 47D03 It is proved that: each collectively order continuous set of operators from an Archimedean OVS with a generating cone to an OVS is collectively order bounded; and each collectively order to norm bounded set of operators from an ordered Banach space with a closed generating cone to a normed space is norm bounded. Several applications to commutative operator semigroups on ordered vector spaces are given. |
| title | Collective order boundedness of sets of operators between ordered vector spaces |
| topic | Functional Analysis 46A40, 46B42, 47B60, 47D03 |
| url | https://arxiv.org/abs/2410.17030 |