COMPLEX SYMMETRY AND CYCLICITY OF COMPOSITION OPERATORS ON H-2(C+)

摘要

In this article, we completely characterize the complex symmetry, cyclicity, and hypercyclicity of composition operators C(phi)f = f omicron phi induced by affine self-maps phi of the right half-plane C+ on the Hardy-Hilbert space H-2(C+). The interplay between complex symmetry and cyclicity plays a key role in the analysis. We also provide new proofs for the normal, self-adjoint, and unitary cases and for an adjoint formula discovered by Gallardo-Gutierrez and Montes-Rodriguez.