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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2605.21982 |
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| _version_ | 1866911704198152192 |
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| author | Araiza, Roy Oikhberg, Timur |
| author_facet | Araiza, Roy Oikhberg, Timur |
| contents | We investigate the category of ``matricial order operator spaces,'' which generalize operator systems, being equipped with both matricial norms and matricial order. For these objects, we develop duality theory. Taking a cue from the theory of ordered normed spaces, we introduce two important properties describing the interplay between order and norm -- ``normality'' and ``generation,'' and show that they are dual to each other. As examples, we consider operator systems (in particular, C*-algebras), and Schatten spaces. We also describe the minimal and maximal matricial order structures (which, again, turn out to be in duality), and show how Banach lattices can be equipped with such structures. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_21982 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On Matricial Order Operator Spaces Araiza, Roy Oikhberg, Timur Functional Analysis 46L07, 46B40 We investigate the category of ``matricial order operator spaces,'' which generalize operator systems, being equipped with both matricial norms and matricial order. For these objects, we develop duality theory. Taking a cue from the theory of ordered normed spaces, we introduce two important properties describing the interplay between order and norm -- ``normality'' and ``generation,'' and show that they are dual to each other. As examples, we consider operator systems (in particular, C*-algebras), and Schatten spaces. We also describe the minimal and maximal matricial order structures (which, again, turn out to be in duality), and show how Banach lattices can be equipped with such structures. |
| title | On Matricial Order Operator Spaces |
| topic | Functional Analysis 46L07, 46B40 |
| url | https://arxiv.org/abs/2605.21982 |