Bulletin of the Belgian Mathematical Society - Simon Stevin

Hypercyclic behaviour of multiples of composition operators on weighted Banach spaces of holomorphic functions

Yu-Xia Liang and Ze-Hua Zhou

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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 $H_{\alpha,0}^\infty$.

Article information

Source
Bull. Belg. Math. Soc. Simon Stevin, Volume 21, Number 3 (2014), 385-401.

Dates
First available in Project Euclid: 11 August 2014

Permanent link to this document
https://projecteuclid.org/euclid.bbms/1407765879

Mathematical Reviews number (MathSciNet)
MR3250768

Zentralblatt MATH identifier
1305.60104

Subjects
Primary: 47A16: Cyclic vectors, hypercyclic and chaotic operators
Secondary: 47B38: Operators on function spaces (general) 47B37: Operators on special spaces (weighted shifts, operators on sequence spaces, etc.)

Keywords
hypercyclic composition operator weighted Banach space

Citation

Liang, Yu-Xia; Zhou, Ze-Hua. Hypercyclic behaviour of multiples of composition operators on weighted Banach spaces of holomorphic functions. Bull. Belg. Math. Soc. Simon Stevin 21 (2014), no. 3, 385--401. https://projecteuclid.org/euclid.bbms/1407765879


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