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arXiv · 1908.08592

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

S. Waleed Noor·Osmar R. Severiano
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Abstract

In this article, we completely characterize the complex symmetry, cyclicity and hypercyclicity of composition operators $C_ϕf=f\circϕ$ induced by affine self-maps $ϕ$ 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.

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S. Waleed Noor, Osmar R. Severiano. 2019-10-11. Complex symmetry and cyclicity of composition operators on $H^2(\mathbb{C}_+)$. https://arxiv.org/abs/1908.08592

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