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).
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Format: | Article |
Language: | English |
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De Gruyter
2022-06-01
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Series: | Concrete Operators |
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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). |
first_indexed | 2024-04-10T21:31:36Z |
format | Article |
id | doaj.art-50a150e2dcfc48a895abd4209961354c |
institution | Directory Open Access Journal |
issn | 2299-3282 |
language | English |
last_indexed | 2024-04-10T21:31:36Z |
publishDate | 2022-06-01 |
publisher | De Gruyter |
record_format | Article |
series | Concrete Operators |
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 |