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 $\mathbb{R}^\infty$. We introduce weak cohyponormality classes $\EuScript{S}_{n,r}^*$ of unbounded operators and provide criteria for the aforementioned composition operators to belong to $\EuScript{S}_{n,r}^*$. Our approach is based on inductive limits of operators.