Composition operators between two different bilateral grand Lebesgue spaces

TL;DR

This paper studies the properties of composition operators acting between two different Grand Lebesgue Spaces, focusing on their boundedness, compactness, and essential norm, which are key for understanding their functional behavior.

Contribution

It provides new criteria for the boundedness, compactness, and essential norm of composition operators between different GLS, expanding the theoretical understanding of these operators.

Findings

Established conditions for boundedness of composition operators.

Derived criteria for compactness of these operators.

Analyzed the essential norm in the context of GLS.

Abstract

In this paper we consider composition operator generated by nonsingular measurable transformation between two different Grand Lebesgue Spaces (GLS); we investigate the boundedness, compactness and essential norm of composition operators.