
In the paper under review, the author is concerned with the dynamics of the weighted composition operator \(C_{\omega,\varphi}: H(\Omega)\to H(\Omega)\) given by \(C_{\omega,\varphi}(f)(z)=\omega(z)(f\circ \varphi)(z)\), for \(z\in \Omega\), where \(H(\Omega)\) denotes the space of holomorphic functions on a simply connected domain \(\Omega\) of the complex field, endowed with the compact open topology, \(\varphi\) is a holomorphic self map of \(\Omega\), and \(\omega\in H(\Omega)\). In particular, the author shows that any such operator \(C_{\omega,\varphi}\) is weakly supercyclic if and only if it is topologically mixing and, in the case that the weight is bounded, if and only if the operator has a hypercyclic subspace. The author also provides conditions on the symbol in order that the operator \(C_{\omega,\varphi}\) is Devaney-chaotic and has a frequently hypercyclic subspace.
chaotic operators, composition operators, Linear composition operators, Physical Sciences and Mathematics, Cyclic vectors, hypercyclic and chaotic operators, Compositional universality, supercyclic operators, hypercyclic operators
chaotic operators, composition operators, Linear composition operators, Physical Sciences and Mathematics, Cyclic vectors, hypercyclic and chaotic operators, Compositional universality, supercyclic operators, hypercyclic operators
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