Unbounded composition operators on Orlicz spaces

TL;DR

This paper investigates the properties of unbounded composition operators on Orlicz spaces, providing criteria for their dense definability, adjoint properties, and conditions for continuity and boundedness.

Contribution

It offers new necessary and sufficient conditions for when composition operators on Orlicz spaces are densely defined, continuous, and characterizes their adjoints.

Findings

Criteria for dense definability of composition operators

Conditions for the continuity of densely defined operators

Characterization of densely defined continuous composition operators

Abstract

In this paper we deal with unbounded composition operators defined in Orlicz spaces. Indeed, we provide some necessary and sufficient condition for densely definedness of composition operators on Orlicz spaces. Also, we will investigate the adjoint of densely defined composition operators and we give some equivalent conditions for it to be densely defined. In addition, we show that densely defined composition operator is continuous if and only if it is everywhere defined. Finally, we characterize densely defined continuous composition operators.