Complex symmetry and cyclicity of composition operators on 𝐻²(ℂ₊)

Noor, S.; Severiano, Osmar

doi:10.1090/proc/14918

Complex symmetry and cyclicity of composition operators on $H^2(\mathbb {C}_+)$
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by S. Waleed Noor and Osmar R. Severiano

Proc. Amer. Math. Soc. 148 (2020), 2469-2476

DOI: https://doi.org/10.1090/proc/14918

Published electronically: January 29, 2020

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Abstract:

In this article, we completely characterize the complex symmetry, cyclicity, and hypercyclicity of composition operators $C_\phi f=f\circ \phi$ induced by affine self-maps $\phi$ of the right half-plane $\mathbb {C}_+$ on the Hardy-Hilbert space $H^2(\mathbb {C}_+)$. 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-Gutiérrez and Montes-Rodríguez.

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