Weighted composition operators induced by linear fractional maps with the 2-complex symmetric property

A. Singh, M. Sharma

We investigate weighted composition operators Wψ,φ induced by linear fractional maps with the 2-complex symmetric property acting on the Hardy space H2(ⅅ) relative to the conjugation operator J: H2(ⅅ) → H2(ⅅ) given by (Jf)(z) = f( z ) , f ∊ H2(ⅅ), in a special case when φ is assumed to be a linear fractional self-map of ⅅ , and the weight function ψ is chosen as the reproducing kernel centred at the point σ(0), i.e., ψ = Kσ(0), where σ denotes Cowen’s auxiliary function associated with φ . We find necessary and sufficient criteria ensuring that the weighted composition operator satisfies the 2-complex symmetric relation. 

Advanced Studies: Euro-Tbilisi Mathematical Journal, Vol. 19(2) (2026), pp. 71-85