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On the isomorphism class of q-Gaussian W * -algebras for infinite variables
Caspers, Martijn1
1 TU Delft, EWI/DIAM, P.O.Box 5031, 2600 GA Delft, The Netherlands
Comptes Rendus. Mathématique, Tome 361 (2023) no. G11, pp. 1711-1716

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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

Caspers, Martijn 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},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {1711--1716},
     publisher = {Acad\'emie des sciences, Paris},
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     doi = {10.5802/crmath.489},
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Caspers, Martijn. On the isomorphism class of $q$-Gaussian W$^\ast $-algebras for infinite variables. Comptes Rendus. Mathématique, Tome 361 (2023) no. G11, pp. 1711-1716. doi: 10.5802/crmath.489

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