Normal complex symmetric weighted composition operators on the Hardy space

Abstract

In this paper, we investigate the normal weighed composition operators W ψ,ϕ which is J −symmetric, C 1 −symmetric and C 2 −symmetric on the Hardy space H 2 (D) respectively. Firstly, equivalent conditions of the normality of C 1 −symmetric and C 2 −symmetric weighted composition operators on H 2 (D) is given. Furthermore, the normal J −symmetric, C 1 −symmetric and C 2 −symmetric weighted composition operators on H 2 (D) when ϕ has an interior fixed point, ϕ is of hyperbolic type or parabolic type are respectively investigated.