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

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).

Keywords

• bounded product
• densely defined
• composition operators
• l2-space
• normality
• quasinormality
• primary 47b33, 47b20
• secondary 47a05, 47b37