Affiliation:
1. Department of Mathematics, Ondokuz Mayıs University, Faculty of Sciences, Kurupelit campus, 55139 Atakum-Samsun, TURKEY
Abstract
This paper investigates the behavior and structural properties of composition operators within the framework of 𝔹ℂ-rearrangement 𝔹ℂ-module spaces. Building upon the foundational concepts of 𝔹ℂ-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 𝔹ℂ -modules and 𝔹ℂ-rearrangement-invariant spaces and laying the groundwork for our subsequent analysis, a rigorous examination of composition operators, we uncover fundamental properties such as 𝔻-continuity, 𝔻- boundedness, and 𝔻-compactness, shedding light on the intrinsic characteristics of these operators within 𝔹ℂmodule spaces.
Publisher
World Scientific and Engineering Academy and Society (WSEAS)
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