On the isomorphism class of $q$-Gaussian W$^\ast $-algebras for infinite variables
Let $M_q(H_{\mathbb{R}})$ be the $q$-Gaussian von Neumann algebra associated with a separable infinite dimensional real Hilbert space $H_{\mathbb{R}}$ where $-1 < q < 1$. We show that $M_q(H_{\mathbb{R}}) \lnot \simeq M_0(H_{\mathbb{R}})$ for $-1 < q \ne 0 < 1$. The C$^\ast $-algebraic...
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Académie des sciences
2023-12-01
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| Series: | Comptes Rendus. Mathématique |
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| Online Access: | https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.489/ |
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| author | Caspers, Martijn |
| author_facet | Caspers, Martijn |
| author_sort | Caspers, Martijn |
| collection | DOAJ |
| description | Let $M_q(H_{\mathbb{R}})$ be the $q$-Gaussian von Neumann algebra associated with a separable infinite dimensional real Hilbert space $H_{\mathbb{R}}$ where $-1 < q < 1$. We show that $M_q(H_{\mathbb{R}}) \lnot \simeq M_0(H_{\mathbb{R}})$ for $-1 < q \ne 0 < 1$. The C$^\ast $-algebraic counterpart of this result was obtained recently in [1]. Using ideas of Ozawa we show that this non-isomorphism result also holds on the level of von Neumann algebras. |
| format | Article |
| id | doaj-art-474dd760d3214eb9b4987b921baa21c2 |
| institution | Kabale University |
| issn | 1778-3569 |
| language | English |
| publishDate | 2023-12-01 |
| publisher | Académie des sciences |
| record_format | Article |
| series | Comptes Rendus. Mathématique |
| spelling | doaj-art-474dd760d3214eb9b4987b921baa21c22025-02-07T11:12:14ZengAcadémie des sciencesComptes Rendus. Mathématique1778-35692023-12-01361G111711171610.5802/crmath.48910.5802/crmath.489On the isomorphism class of $q$-Gaussian W$^\ast $-algebras for infinite variablesCaspers, Martijn0TU Delft, EWI/DIAM, P.O.Box 5031, 2600 GA Delft, The NetherlandsLet $M_q(H_{\mathbb{R}})$ be the $q$-Gaussian von Neumann algebra associated with a separable infinite dimensional real Hilbert space $H_{\mathbb{R}}$ where $-1 < q < 1$. We show that $M_q(H_{\mathbb{R}}) \lnot \simeq M_0(H_{\mathbb{R}})$ for $-1 < q \ne 0 < 1$. The C$^\ast $-algebraic counterpart of this result was obtained recently in [1]. Using ideas of Ozawa we show that this non-isomorphism result also holds on the level of von Neumann algebras.https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.489/$q$-Gaussian von Neumann algebrasAkemann–Ostrand property |
| spellingShingle | Caspers, Martijn On the isomorphism class of $q$-Gaussian W$^\ast $-algebras for infinite variables Comptes Rendus. Mathématique $q$-Gaussian von Neumann algebras Akemann–Ostrand property |
| title | On the isomorphism class of $q$-Gaussian W$^\ast $-algebras for infinite variables |
| title_full | On the isomorphism class of $q$-Gaussian W$^\ast $-algebras for infinite variables |
| title_fullStr | On the isomorphism class of $q$-Gaussian W$^\ast $-algebras for infinite variables |
| title_full_unstemmed | On the isomorphism class of $q$-Gaussian W$^\ast $-algebras for infinite variables |
| title_short | On the isomorphism class of $q$-Gaussian W$^\ast $-algebras for infinite variables |
| title_sort | on the isomorphism class of q gaussian w ast algebras for infinite variables |
| topic | $q$-Gaussian von Neumann algebras Akemann–Ostrand property |
| url | https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.489/ |
| work_keys_str_mv | AT caspersmartijn ontheisomorphismclassofqgaussianwastalgebrasforinfinitevariables |