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

TL;DR

This paper proves that in mixed q-Gaussian algebras, the generator subalgebra exhibits singularity, advancing understanding of their algebraic structure.

Contribution

It establishes the singularity of the generator subalgebra in mixed q-Gaussian algebras, a novel result in the study of these operator algebras.

Findings

Generator subalgebra is singular in mixed q-Gaussian algebras.

Results apply to algebras with symmetric matrices Q where |q_{ij}|<1.

Enhances understanding of the structure of 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.