Supercyclicity and Resolvent Condition for Weighted Composition Operators
Peer reviewed, Journal article
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2021Metadata
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Mengestie, T., & Seyoum, W. (2021). Supercyclicity and resolvent condition for weighted composition operators. Computational Methods and Function Theory. 10.1007/s40315-021-00380-xAbstract
For pairs of holomorphic maps(u,ψ) on the complex plane, we study some dynamical properties of the weighted composition operator W(u,ψ) on the Fock spaces. We prove that no weighted composition operator on the Fock spaces is supercyclic. Conditions under which the operators satisfy the Ritt’s resolvent growth condition are also identified. In particular, we show that a non-trivial composition operator on the Fock spaces satisfies such a growth condition if and only if it is compact.