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

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).

Bibliographic Details
Main Author: Zhou Hang
Format: Article
Language:English
Published: De Gruyter 2022-06-01
Series:Concrete Operators
Subjects:
Online Access:https://doi.org/10.1515/conop-2022-0130
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author Zhou Hang
author_facet Zhou Hang
author_sort Zhou Hang
collection DOAJ
description 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).
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spelling doaj.art-50a150e2dcfc48a895abd4209961354c2023-01-19T13:20:29ZengDe GruyterConcrete Operators2299-32822022-06-0191869510.1515/conop-2022-0130Normality and Quasinormality of Specific Bounded Product of Densely Defined Composition Operators in L2 SpacesZhou Hang0School of Information Technology and Engineering, Guangzhou College of Commerce, Guangzhou, G. D. 511363, P.R.ChinaLet (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).https://doi.org/10.1515/conop-2022-0130bounded productdensely definedcomposition operatorsl2-spacenormalityquasinormalityprimary 47b33, 47b20secondary 47a05, 47b37
spellingShingle Zhou Hang
Normality and Quasinormality of Specific Bounded Product of Densely Defined Composition Operators in L2 Spaces
Concrete Operators
bounded product
densely defined
composition operators
l2-space
normality
quasinormality
primary 47b33, 47b20
secondary 47a05, 47b37
title Normality and Quasinormality of Specific Bounded Product of Densely Defined Composition Operators in L2 Spaces
title_full Normality and Quasinormality of Specific Bounded Product of Densely Defined Composition Operators in L2 Spaces
title_fullStr Normality and Quasinormality of Specific Bounded Product of Densely Defined Composition Operators in L2 Spaces
title_full_unstemmed Normality and Quasinormality of Specific Bounded Product of Densely Defined Composition Operators in L2 Spaces
title_short Normality and Quasinormality of Specific Bounded Product of Densely Defined Composition Operators in L2 Spaces
title_sort normality and quasinormality of specific bounded product of densely defined composition operators in l2 spaces
topic bounded product
densely defined
composition operators
l2-space
normality
quasinormality
primary 47b33, 47b20
secondary 47a05, 47b37
url https://doi.org/10.1515/conop-2022-0130
work_keys_str_mv AT zhouhang normalityandquasinormalityofspecificboundedproductofdenselydefinedcompositionoperatorsinl2spaces