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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 Mq(Hℝ) be the q-Gaussian von Neumann algebra associated with a separable infinite dimensional real Hilbert space Hℝ where -1<q<1. We show that Mq(Hℝ)¬≃M0(Hℝ) 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
Mots-clés : 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
Licence : CC-BY 4.0
Droits d'auteur : Les auteurs conservent leurs droits 
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     title = {On the isomorphism class of $q${-Gaussian} {W}$^\ast $-algebras for infinite variables},
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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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