Continuous Selection of Unitaries in II$_1$ Factors
Fuente:
arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866918140873539584 |
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| author | Farah, Ilijas Vaccaro, Andrea |
| author_facet | Farah, Ilijas Vaccaro, Andrea |
| contents | We prove continuous-valued analogues of the basic fact that Murray-von Neumann subequivalence of projections in II$_1$ factors is completely determined by tracial evaluations. We moreover use this result to solve the so-called trace problem in the case of factorial trivial $W^\ast$-bundles whose base space has covering dimension at most 1. Our arguments are based on applications of a continuous selection theorem due to Michael to von Neumann algebras. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_01272 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Continuous Selection of Unitaries in II$_1$ Factors Farah, Ilijas Vaccaro, Andrea Operator Algebras 46L05, 46L10 We prove continuous-valued analogues of the basic fact that Murray-von Neumann subequivalence of projections in II$_1$ factors is completely determined by tracial evaluations. We moreover use this result to solve the so-called trace problem in the case of factorial trivial $W^\ast$-bundles whose base space has covering dimension at most 1. Our arguments are based on applications of a continuous selection theorem due to Michael to von Neumann algebras. |
| title | Continuous Selection of Unitaries in II$_1$ Factors |
| topic | Operator Algebras 46L05, 46L10 |
| url | https://arxiv.org/abs/2501.01272 |