Composition Operators between BC-rearrangement Invariant BC-Module Spaces

This paper investigates the behavior and structural properties of composition operators within the framework of ℂ-rearrangement ℂ-module spaces. Building upon the foundational concepts of ℂ-modules and rearrangement-invariant spaces, we explore the intricate interplay between these spaces under the action of composition operators. Our study delves into the algebraic and topological aspects of composition operators, elucidating their impact on the underlying space structures. After establishing the necessary background on ℂ -modules and ℂ-rearrangement-invariant spaces and laying the groundwork for our subsequent analysis, a rigorous examination of composition operators, we uncover fundamental properties such as -continuity, - boundedness, and -compactness, shedding light on the intrinsic characteristics of these operators within ℂmodule spaces.