Which weighted composition operators are hyponormal on the Hardy and weighted Bergman spaces?
Fatehi, Mahsa · Shaabani, Mahmood Haji
Original · EN
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 Cψ,ᵩ on H² and A²α. Next, we show that for φ∈ LFT(D), if Cφ is hyponormal on H² or A²α, 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 Cφ on H² and A²α, when φ has a Denjoy-Wolff point ζ∈ ∂ D. Finally, descriptions of spectral radii are provided for some hyponormal weighted composition operators on H² and A²α.
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