On an example of a complex symmetric composition operator on H2(D)

Complex symmetric composition operators induced by linear fractional maps

“…Sungeun Jung et al [3] posed a non-automorphic example of composition operator which was thought to be complex symmetric, but then it was disproved by Waleed Noor in [10]. Recently, Narayan et al [4] gave the first non-automorphic examples of complex symmetric composition operators.…”

Complex symmetric weighted composition operators on the Hardy space

“…By making unitary transformations, Jung et al [11] provided some more examples. For more work on complex symmetric composition operators, see [2,10,14,15]. In this paper, we will make a slight generalization of Jung's result.…”

Complex symmetric composition operators on a Hilbert space of Dirichlet series

“…Then the authors [13] studied complex symmetric weighted composition operators for some special conjugation on the classical Hardy space H 2 (D) over the unit disk D. Recently, Narayan-Sievewright-Thompson [14] gave complex symmetric composition operators on H 2 (D) whose symbols are linear-fractional but not automorphic. As an application, that answered the question of Noor [17]: Does there exist a non-constant and non-automorphic symbol φ for which C φ is complex symmetric but not normal on H 2 (D)?…”