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Functional analysis
On the isomorphism class of q-Gaussian W * -algebras for infinite variables
Martijn Caspers1
1 TU Delft, EWI/DIAM, P.O.Box 5031, 2600 GA Delft, The Netherlands
Comptes Rendus. Mathématique, Volume 361 (2023), pp. 1711-1716.

Let M q (H ℝ ) be the q-Gaussian von Neumann algebra associated with a separable infinite dimensional real Hilbert space H ℝ where -1<q<1. We show that M q (H ℝ )¬≃M 0 (H ℝ ) for -1<q≠0<1. The C * -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.

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DOI: 10.5802/crmath.489
Classification: 46L35, 46L06
Keywords: $q$-Gaussian von Neumann algebras, Akemann–Ostrand property

Martijn Caspers 1

1 TU Delft, EWI/DIAM, P.O.Box 5031, 2600 GA Delft, The Netherlands
License: CC-BY 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights 
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Martijn Caspers. On the isomorphism class of $q$-Gaussian W$^\ast $-algebras for infinite variables. Comptes Rendus. Mathématique, Volume 361 (2023), pp. 1711-1716. doi : 10.5802/crmath.489. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.489/

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