Soft inductive limits of operator systems and a noncommutative Lazar-Lindenstrauss theorem
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866914071704502272 |
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| author | Courtney, Kristin Galke, Niklas van Luijk, Lauritz Stottmeister, Alexander |
| author_facet | Courtney, Kristin Galke, Niklas van Luijk, Lauritz Stottmeister, Alexander |
| contents | We establish a flexible generalization of inductive systems of operator systems, which relaxes the usual transitivity (or coherence) condition to an asymptotic version thereof and allows for systems indexed over arbitrary nets. To illustrate the utility of this generalization, we highlight how such systems arise naturally from completely positive approximations of nuclear operator systems. Going further, we utilize an argument of Ding and Peterson to show that a separable operator system is nuclear if and only if it is an inductive limit of matrix algebras, generalizing a classic Theorem of Lazar and Lindenstrauss to the setting of noncommutative Choquet theory. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_02019 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Soft inductive limits of operator systems and a noncommutative Lazar-Lindenstrauss theorem Courtney, Kristin Galke, Niklas van Luijk, Lauritz Stottmeister, Alexander Operator Algebras 46L07, 46A55 We establish a flexible generalization of inductive systems of operator systems, which relaxes the usual transitivity (or coherence) condition to an asymptotic version thereof and allows for systems indexed over arbitrary nets. To illustrate the utility of this generalization, we highlight how such systems arise naturally from completely positive approximations of nuclear operator systems. Going further, we utilize an argument of Ding and Peterson to show that a separable operator system is nuclear if and only if it is an inductive limit of matrix algebras, generalizing a classic Theorem of Lazar and Lindenstrauss to the setting of noncommutative Choquet theory. |
| title | Soft inductive limits of operator systems and a noncommutative Lazar-Lindenstrauss theorem |
| topic | Operator Algebras 46L07, 46A55 |
| url | https://arxiv.org/abs/2510.02019 |