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J. Korean Math. Soc. 2011; 48(5): 969-984

Printed September 1, 2011

https://doi.org/10.4134/JKMS.2011.48.5.969

Copyright © The Korean Mathematical Society.

Hypercyclicity of weighted composition operators on the unit ball of $\mathbb{C}^{N}$

Ren-Yu Chen and Ze-Hua Zhou

Tianjin University, Tianjin University

Abstract

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This paper discusses the hypercyclicity of weighted composition operators acting on the space of holomorphic functions on the open unit ball $B_{N}$ of $\mathbb{C}^{N}$. Several analytic properties of linear fractional self-maps of $B_{N}$ are given. According to these properties, a few necessary conditions for a weighted composition operator to be hypercyclic in the space of holomorphic functions are proved. Besides, the hypercyclicity of adjoint of weighted composition operators are studied in this paper.

Keywords: hypercyclic operator, weighted composition operator, linear fractional map, generalized Cayley transform, Heisenberg transform, Denjoy-Wollf point

MSC numbers: Primary 47B33; Secondary 47B35, 47B38, 46E15, 32A36

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