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Singularity of the generator subalgebra in mixed $q$-Gaussian algebras

Volume 158 / 2019

Simeng Wang Colloquium Mathematicum 158 (2019), 39-43 MSC: Primary 46L36, 46L53, 81S05. DOI: 10.4064/cm7677-9-2018 Published online: 14 June 2019

Abstract

We prove that for the mixed $q$-Gaussian algebra $\varGamma _{Q}(H_{\mathbb {R}})$ associated to a real Hilbert space $H_{\mathbb {R}}$ and a real symmetric matrix $Q=(q_{ij})$ with $\operatorname {sup}|q_{ij}| \lt 1$, the generator subalgebra is singular.

Authors

  • Simeng WangFachbereich Mathematik
    Saarland University
    Postfach 151150
    66041 Saarbrücken, Germany
    e-mail

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