Let ϕ be an analytic self-map of the open unit disk D. We study the complex symmetry of composition operators Cϕ on weighted Hardy spaces induced by a bounded sequence. For any analytic self-map of D that is not an elliptic automorphism, we establish that if Cϕ is complex symmetric, then either ϕ(0) = 0 or ϕ is linear. In the case of weighted Bergman spaces A2 α, we find the non-automorphic linear fractional symbols ϕ such that Cϕ is complex symmetric.
|Journal||Proceedings of the American Mathematical Society|
|State||Published - 2020|