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

TL;DR

This paper studies unbounded composition operators with infinite matrix symbols in Gaussian $L^2$-spaces, introducing new classes and criteria for weak cohyponormality using inductive limits.

Contribution

It introduces weak cohyponormality classes for unbounded operators and provides criteria for composition operators to belong to these classes, advancing the understanding of their structure.

Findings

Criteria for composition operators to be in $ ext{S}_{n,r}^*$ classes.

Development of inductive limit approach for unbounded operators.

Characterization of cosubnormal operators with matrix symbols.

Abstract

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.