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

Abstract

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

3 pages