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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2501.16832 |
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| _version_ | 1866911193548980224 |
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| author | Choi, Ikhan |
| author_facet | Choi, Ikhan |
| contents | We affirmatively resolve a question posed by Uffe Haagerup in 1975 on the positive version of the bipolar theorem on the dual spaces of C$^*$-algebras. As a direct consequence, we obtain a complete set of four positive Hahn-Banach separation theorems on von Neumann algebras, their preduals, C$^*$-algebras, and their duals. Furthermore, with the idea used to solve the problem, we simplify Haagerup's original solution to Dixmier's problem on normal weights. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_16832 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A solution to Haagerup's problem and positive Hahn-Banach separation theorems in operator algebras Choi, Ikhan Operator Algebras Functional Analysis 46L05, 46L10, 47L50 We affirmatively resolve a question posed by Uffe Haagerup in 1975 on the positive version of the bipolar theorem on the dual spaces of C$^*$-algebras. As a direct consequence, we obtain a complete set of four positive Hahn-Banach separation theorems on von Neumann algebras, their preduals, C$^*$-algebras, and their duals. Furthermore, with the idea used to solve the problem, we simplify Haagerup's original solution to Dixmier's problem on normal weights. |
| title | A solution to Haagerup's problem and positive Hahn-Banach separation theorems in operator algebras |
| topic | Operator Algebras Functional Analysis 46L05, 46L10, 47L50 |
| url | https://arxiv.org/abs/2501.16832 |