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arXiv · 2210.11128

On the isomorphism class of $q$-Gaussian W$^\ast$-algebras for infinite variables

Martijn Caspers
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Abstract

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 $M_q(H_{\mathbb{R}}) \not \simeq M_0(H_{\mathbb{R}})$ for $-1 < q \not = 0 < 1$. The C$^\ast$-algebraic counterpart of this result was obtained recently in [BCKW22]. Using ideas of Ozawa we show that this non-isomorphism result also holds on the level of von Neumann algebras.

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Martijn Caspers. 2022-10-20. On the isomorphism class of $q$-Gaussian W$^\ast$-algebras for infinite variables. https://arxiv.org/abs/2210.11128

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