Complex symmetry and cyclicity of composition operators on $H^2({\mathbb{C}}_{+})$

Abstract

In this article, we completely characterize the complex symmetry, cyclicity and hypercyclicity of composition operators $C_{\varphi }f=f\circ \varphi$ induced by affine self-maps $\varphi$ of the right half-plane ${\mathbb{C}}_{+}$ on the Hardy-Hilbert space $H^2({\mathbb{C}}_{+})$. We also provide new proofs for the normal, self-adjoint and unitary cases and for an adjoint formula discovered by Gallardo-Gutiérrez and Montes-Rodrígues.

8 pages, to appear in Proc. Amer. Math. Soc