Abstract
A Furstenberg family \(\mathcal{F}\) is a collection of infinite subsets ofthe set of positive integers such that if \(A\subset B\) and \(A\in \mathcal{F}\), then \(B\in \mathcal{F}\). For aFurstenberg family \(\mathcal{F}\), an operator \(T\) on a topological vector space \(X\) is said tobe \(\mathcal{F}\)-transitive provided that for each non-empty open subsets \(U\), \(V\) of \(X\) the set\(\{n \in \mathbb{N}: T^n (U) \cap V \neq\emptyset\}\) belongs to \(\mathcal{F}\). In this paper, we characterize the \(\mathcal{F}\)-transitivityof composition operator \(C_\phi\) on the space \(H(\Omega)\) of holomorphic functionson a domain \(\Omega\subset \mathbb{C}\) by providing a necessary and sufficient condition in terms ofthe symbol \(\phi\).
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The authors would like to express their sincere thanks to the referee for the generous and accurate refereeing process and valuable comments and suggestions on this paper. They are indebted to the referee for the very precise reading of the manuscript.
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Amouch, M., Karim, N. Strong transitivity of composition operators. Acta Math. Hungar. 164, 458–469 (2021). https://doi.org/10.1007/s10474-021-01140-y
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DOI: https://doi.org/10.1007/s10474-021-01140-y