Normality and Quasinormality of Specific Bounded Product of Densely Defined Composition Operators in L2 Spaces

IF 0.3 Q4 MATHEMATICS Concrete Operators Pub Date : 2022-01-01 DOI:10.1515/conop-2022-0130
Hang Zhou
{"title":"Normality and Quasinormality of Specific Bounded Product of Densely Defined Composition Operators in L2 Spaces","authors":"Hang Zhou","doi":"10.1515/conop-2022-0130","DOIUrl":null,"url":null,"abstract":"Abstract Let (X, 𝒜, μ) be a σ−finite measure space. A transformation ϕ : X → X is non-singular if μ ∘ ϕ−1 is absolutely continuous with respect with μ. For this non-singular transformation, the composition operator Cϕ: 𝒟(Cϕ) → L2(μ) is defined by Cϕf = f ∘ ϕ, f ∈ 𝒟(Cϕ). For a fixed positive integer n ≥ 2, basic properties of product Cϕn · · · Cϕ1 in L2(μ) are presented in Section 2, including the boundedness and adjoint. Under the assistance of these properties, normality and quasinormality of specific bounded Cϕn · · · Cϕ1 in L2(μ) are characterized in Section 3 and 4 respectively, where Cϕ1, Cϕ2, · · ·, Cϕn are all densely defined.","PeriodicalId":53800,"journal":{"name":"Concrete Operators","volume":null,"pages":null},"PeriodicalIF":0.3000,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Concrete Operators","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1515/conop-2022-0130","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0

Abstract

Abstract Let (X, 𝒜, μ) be a σ−finite measure space. A transformation ϕ : X → X is non-singular if μ ∘ ϕ−1 is absolutely continuous with respect with μ. For this non-singular transformation, the composition operator Cϕ: 𝒟(Cϕ) → L2(μ) is defined by Cϕf = f ∘ ϕ, f ∈ 𝒟(Cϕ). For a fixed positive integer n ≥ 2, basic properties of product Cϕn · · · Cϕ1 in L2(μ) are presented in Section 2, including the boundedness and adjoint. Under the assistance of these properties, normality and quasinormality of specific bounded Cϕn · · · Cϕ1 in L2(μ) are characterized in Section 3 and 4 respectively, where Cϕ1, Cϕ2, · · ·, Cϕn are all densely defined.
查看原文
分享 分享
微信好友 朋友圈 QQ好友 复制链接
本刊更多论文
L2空间中密定义复合算子的特定有界积的正态性和拟不规则性
摘要设(X, φ, μ)是一个σ−有限测度空间。如果μ°φ - 1相对于μ绝对连续,则变换φ: X→X是非奇异的。对于这个非奇异变换,复合算子Cϕ: (Cϕ)→L2(μ)定义为Cϕf = f°φ, f∈(Cϕ)。对于固定正整数n≥2,在第2节中给出了L2(μ)中积c_ (n···c_(1))的基本性质,包括有界性和伴随性。在这些性质的帮助下,在第3节和第4节中分别描述了L2(μ)中特定有界的c_ (n···)c_(1)的正态性和拟不规则性,其中c_(1)、c_(2)、··、c_ (n)都是密集定义的。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
求助全文
约1分钟内获得全文 去求助
来源期刊
Concrete Operators
Concrete Operators MATHEMATICS-
CiteScore
1.00
自引率
16.70%
发文量
10
审稿时长
22 weeks
期刊最新文献
On the compactness and the essential norm of operators defined by infinite tridiagonal matrices m-Isometric tensor products Estimation of coefficient bounds for a subclass of Sakaguchi kind functions mapped onto various domains Generalized Crofoot transform and applications Generalized Hausdorff operator on Bergmann spaces
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
×
提示
您的信息不完整,为了账户安全,请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
现在去查看 取消
×
提示
确定
0
微信
客服QQ
Book学术公众号 扫码关注我们
反馈
×
意见反馈
请填写您的意见或建议
请填写您的手机或邮箱
已复制链接
已复制链接
快去分享给好友吧!
我知道了
×
扫码分享
扫码分享
Book学术官方微信
Book学术文献互助
Book学术文献互助群
群 号:481959085
Book学术
文献互助 智能选刊 最新文献 互助须知 联系我们:info@booksci.cn
Book学术提供免费学术资源搜索服务,方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。
Copyright © 2023 Book学术 All rights reserved.
ghs 京公网安备 11010802042870号 京ICP备2023020795号-1