Complex symmetric composition operators on the Newton space

Abstract

A conjecture posed by MacDonald and Rosenthal states the composition operator Cφ acting on the Newton space N2(P) induced by φ(z)=mz+m−12 is bounded, where m∈(0,1). Our first result is proving that the aforementioned conjecture holds. We investigate complex symmetry of composition operators acting on the Newton space, which is different from that on the Hardy space. In addition, normality and co-isometry of composition operators are studied. Finally, we consider complex symmetric weighted composition operators.