Singularity of the generator subalgebra in mixed $q$-Gaussian algebras
Volume 158 / 2019
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.
