2-complex symmetric composition operators on $H^2$

Abstract

In this paper, we study 2-complex symmetric composition operators with the conjugation J on the Hardy space H 2 . More precisely, we obtain the necessary and sufficient condition for the composition operator C φ to be 2complex symmetric when the symbols φ is an automorphism of D. We also characterize the 2-complex symmetric composition operator C φ on the Hardy space H 2 when φ is a linear fractional self-map of D.