Dense definiteness and boundedness of composition operators in $L^2$-spaces via inductive limits

TL;DR

This paper investigates the conditions for dense definiteness and boundedness of composition operators in $L^2$-spaces using inductive limits, providing new methods and illustrative examples.

Contribution

It introduces novel methods based on inductive limits and projective systems to analyze composition operators in $L^2$-spaces, advancing theoretical understanding.

Findings

Established criteria for dense definiteness of composition operators

Derived conditions for boundedness using inductive limit techniques

Provided illustrative examples demonstrating the methods

Abstract

The questions of dense definiteness and boundedness of composition operators in $L^2$-spaces are studied by means of inductive limits of operators. Methods based on projective systems of measure spaces and inductive limits of $L^2$-spaces are developed. Illustrative examples are presented.