Fock structure of complete Boolean algebras of type I factors and of unital factorizations
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arXiv
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866909278487445504 |
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| author | Vidmar, Matija |
| author_facet | Vidmar, Matija |
| contents | The factorizable vectors of a complete Boolean algebra of type I factors, acting on a separable Hilbert space, are shown to be total, resolving a conjecture of Araki and Woods. En route, the spectral theory of noise-type Boolean algebras of Tsirelson is cast in the noncommutative language of "factorizations with unit" for which a muti-layered characterization of being "of Fock type" is provided. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2302_11804 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Fock structure of complete Boolean algebras of type I factors and of unital factorizations Vidmar, Matija Operator Algebras Probability Primary: 46L53. Secondary: 60A99 The factorizable vectors of a complete Boolean algebra of type I factors, acting on a separable Hilbert space, are shown to be total, resolving a conjecture of Araki and Woods. En route, the spectral theory of noise-type Boolean algebras of Tsirelson is cast in the noncommutative language of "factorizations with unit" for which a muti-layered characterization of being "of Fock type" is provided. |
| title | Fock structure of complete Boolean algebras of type I factors and of unital factorizations |
| topic | Operator Algebras Probability Primary: 46L53. Secondary: 60A99 |
| url | https://arxiv.org/abs/2302.11804 |