Abstract
Let $S(\mathbb{D})$ be the collection of all the holomorphic self-maps of open unit disk $\mathbb{D}$ of the complex plane $\mathbb{C}$, and $C_{\varphi}$, the composition operator induced by $\varphi\in S(\mathbb{D})$. For $\alpha>0,\;\lambda\in \mathbb{C}$, we give some sufficient and necessary conditions for the hypercyclicity of multiples of composition operators $\lambda C_\varphi$ acting on the weighted Banach spaces of entire functions $H_{\alpha,0}^\infty$. Moreover, we obtain a partial characterization for the frequent hypercyclicity of $\lambda C_\varphi$ on $H_{\alpha,0}^\infty$.
Citation
Yu-Xia Liang. Ze-Hua Zhou. "Hypercyclic behaviour of multiples of composition operators on weighted Banach spaces of holomorphic functions." Bull. Belg. Math. Soc. Simon Stevin 21 (3) 385 - 401, august 2014. https://doi.org/10.36045/bbms/1407765879
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