On normal, formally normal and quasinormal composition operators in $\ell^2$-spaces

TL;DR

This paper investigates unbounded composition operators in discrete measure space $L^2$-spaces, providing characterizations of when these operators are normal, formally normal, or quasinormal.

Contribution

It offers a comprehensive characterization of unbounded composition operators in $L^2$-spaces over discrete measure spaces, focusing on their normality and related properties.

Findings

Characterization of normal composition operators

Criteria for formally normal operators

Conditions for quasinormality in this setting

Abstract

Unbounded composition operators in $L^2$-space over discrete measure spaces are investigated. Normal, formally normal and quasinormal composition operators acting in $L^2$-spaces of this kind are characterized.