Unbounded composition operators via inductive limits: Cosubnormal operators with matrix symbols, II

Abstract

This article deals with unbounded composition operators with infinite matrix symbols acting in $L^2$-spaces with respect to the Gaussian measure on ${\mathbb{R}}^{\infty }$. We introduce weak cohyponormality classes ${\mathcal{S}}_{n,r}^{\ast }$ of unbounded operators and provide criteria for the aforementioned composition operators to belong to ${\mathcal{S}}_{n,r}^{\ast }$. Our approach is based on inductive limits of operators.