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Hypercyclic composition operators on Hv0‐spaces |
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| Authors: | Alejandro Miralles Elke Wolf |
| Institution: | 1. Departament de Matemàtiques & IMAC, Universitat Jaume I, E‐12071 Castelló, Spain;2. Mathematical Institute, University of Paderborn, 33095 Paderborn, Germany. Phone: +49?5251?60?2606, Fax: +49 5251 60 3836 |
| Abstract: | We consider analytic self‐maps φ on $\mathbf {D}$ and prove that the composition operator Cφ acting on $H_{v}^0$ is hypercyclic if φ is an automorphism or a hyperbolic non‐automorphic symbol with no fixed point. We give examples of weights v and parabolic non‐automorphisms φ on $\mathbf {D}$ which yield non‐hypercyclic composition operators Cφ on $H_{v}^0$. |
| Keywords: | Weighted Banach spaces of holomorphic functions composition operators hypercyclic functions (MSC) 2010 47B33 47A16 30H10 |