BC 重排不变 BC 模块空间之间的合成算子

Q3 Mathematics

WSEAS Transactions on Mathematics Pub Date : 2024-07-19 DOI:10.37394/23206.2024.23.46

İ. Eryılmaz

{"title":"BC 重排不变 BC 模块空间之间的合成算子","authors":"İ. Eryılmaz","doi":"10.37394/23206.2024.23.46","DOIUrl":null,"url":null,"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.","PeriodicalId":55878,"journal":{"name":"WSEAS Transactions on Mathematics","volume":"101 20","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-07-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Composition Operators between BC-rearrangement Invariant BC-Module Spaces\",\"authors\":\"İ. Eryılmaz\",\"doi\":\"10.37394/23206.2024.23.46\",\"DOIUrl\":null,\"url\":null,\"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.\",\"PeriodicalId\":55878,\"journal\":{\"name\":\"WSEAS Transactions on Mathematics\",\"volume\":\"101 20\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2024-07-19\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"WSEAS Transactions on Mathematics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.37394/23206.2024.23.46\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"Mathematics\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"WSEAS Transactions on Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.37394/23206.2024.23.46","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"Mathematics","Score":null,"Total":0}

引用次数: 0

摘要

本文在𝔹ℂ重排𝔹ℂ模块空间的框架内研究了组成算子的行为和结构特性。在𝔹ℂ模块和重排不变空间的基础概念上，我们探索了这些空间在组成算子作用下错综复杂的相互作用。我们的研究深入到了组成算子的代数和拓扑方面，阐明了它们对底层空间结构的影响。在建立了关于𝔹ℂ 模块和𝔹ℂ-重排不变空间的必要背景并为后续分析奠定基础之后，我们对组成算子进行了严格的检验，发现了诸如𝔻-连续性、𝔻-有界性和𝔻-紧凑性等基本性质，揭示了这些算子在𝔹ℂ模块空间中的内在特征。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

Composition Operators between BC-rearrangement Invariant BC-Module Spaces

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.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

WSEAS Transactions on Mathematics Mathematics-Discrete Mathematics and Combinatorics

CiteScore

1.30

自引率

0.00%

发文量

期刊介绍： WSEAS Transactions on Mathematics publishes original research papers relating to applied and theoretical mathematics. We aim to bring important work to a wide international audience and therefore only publish papers of exceptional scientific value that advance our understanding of these particular areas. The research presented must transcend the limits of case studies, while both experimental and theoretical studies are accepted. It is a multi-disciplinary journal and therefore its content mirrors the diverse interests and approaches of scholars involved with linear algebra, numerical analysis, differential equations, statistics and related areas. We also welcome scholarly contributions from officials with government agencies, international agencies, and non-governmental organizations.