Structural and non-isomorphism results for $q$-Araki-Woods factors
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866914057303359488 |
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| author | Ding, Changying Tan, Hui |
| author_facet | Ding, Changying Tan, Hui |
| contents | It is proved that the $q$-Araki-Woods factor $Γ_q(\sH_\R, U)''$ associated with a strongly continuous orthogonal representation $U:\R\to \cO(\sH_\R)$ is strongly solid for all $q\in (-1,1)$ if the representation $U$ is almost periodic. We also show that the $q$-Araki-Woods factor $Γ_q(\sH_\R, U)''$ is not isomorphic to any free Araki-Woods factor for any $q\in (-1,1)\setminus\{0\}$ if the representation $U$ has nontrivial weakly mixing part or infinite dimensional almost periodic part with bounded spectrum. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2509_21636 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Structural and non-isomorphism results for $q$-Araki-Woods factors Ding, Changying Tan, Hui Operator Algebras It is proved that the $q$-Araki-Woods factor $Γ_q(\sH_\R, U)''$ associated with a strongly continuous orthogonal representation $U:\R\to \cO(\sH_\R)$ is strongly solid for all $q\in (-1,1)$ if the representation $U$ is almost periodic. We also show that the $q$-Araki-Woods factor $Γ_q(\sH_\R, U)''$ is not isomorphic to any free Araki-Woods factor for any $q\in (-1,1)\setminus\{0\}$ if the representation $U$ has nontrivial weakly mixing part or infinite dimensional almost periodic part with bounded spectrum. |
| title | Structural and non-isomorphism results for $q$-Araki-Woods factors |
| topic | Operator Algebras |
| url | https://arxiv.org/abs/2509.21636 |