Unbounded composition operators via inductive limits: cosubnormal operators with matrix symbols. II

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