$C$-normal weighted composition operators on $H^2$

Abstract

A bounded linear operator T on a separable complex Hilbert space H is called C-normal if there is a conjugation C on H such that CT * TC = T T * . Let ϕ be a linear fractional self-map of D. In this paper, we characterize the necessary and sufficient condition for the composition operator C ϕ and weighted composition operator W ψ,ϕ to be C-normal with a conjugation C and a function ψ.