Quasinormal and Hyponormal Weighted Composition Operators on 
                $$H^2$$
                
                    
                        
                            H
                            2
                        
                    
                
             and 
                $$A^2_{\alpha }$$
                
                    
                        
                            A
                            α
                            2

In this paper, we study hyponormal weighed composition operators on the Hardy and weighted Bergman spaces. For functions ψ ∈ A(D) which are not the zero function, we characterize all hyponormal compact weighted composition operators C ψ,ϕ on H 2 and A 2 α . Next, we show that for ϕ ∈ LFT(D), if C ϕ is hyponormal on H 2 or A 2 α , then ϕ(z) = λz, where |λ| ≤ 1 or ϕ is a hyperbolic non-automorphism with ϕ(0) = 0 and such that ϕ has another fixed point in ∂D. After that, we find the essential spectral radius of C ϕ on H 2 and A 2 α , when ϕ has a Denjoy-Wolff point ζ ∈ ∂D. Finally, descriptions of spectral radii are provided for some hyponormal weighted composition operators on H 2 and A 2 α .

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Isosymmetric composition operators on H2

Yang,

Li,

2023

Filomat

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Quasinormal and Hyponormal Weighted Composition Operators on $$H^2$$ H 2 and $$A^2_{\alpha }$$ A α 2

Cited by 4 publications

References 17 publications

Spectrum of some weighted composition operators

Spectrum of some weighted composition operators

Essentially hyponormal weighted composition operators on the Hardy and weighted Bergman spaces

Isosymmetric composition operators on H2

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