Voiculescu's Theorem in Properly Infinite Factors
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866913969699028992 |
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| author | Hadwin, Donald Ma, Minghui Shen, Junhao |
| author_facet | Hadwin, Donald Ma, Minghui Shen, Junhao |
| contents | In this paper, we investigate Voiculescu's theorem on approximate unitary equivalence in separable properly infinite factors. As applications, we establish the norm-denseness of the set of all reducible operators, prove a generalized Voiculescu's bicommutant theorem and a version of asymptotic bicommutant theorem, and obtain an interesting cohomological result. Additionally, we extend these results to multiplier algebras within separable type $\mathrm{III}$ factors. At last, a concept of the nuclear length is introduced. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_05799 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Voiculescu's Theorem in Properly Infinite Factors Hadwin, Donald Ma, Minghui Shen, Junhao Operator Algebras In this paper, we investigate Voiculescu's theorem on approximate unitary equivalence in separable properly infinite factors. As applications, we establish the norm-denseness of the set of all reducible operators, prove a generalized Voiculescu's bicommutant theorem and a version of asymptotic bicommutant theorem, and obtain an interesting cohomological result. Additionally, we extend these results to multiplier algebras within separable type $\mathrm{III}$ factors. At last, a concept of the nuclear length is introduced. |
| title | Voiculescu's Theorem in Properly Infinite Factors |
| topic | Operator Algebras |
| url | https://arxiv.org/abs/2403.05799 |