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
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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.
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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。
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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
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