Disjoint strong transitivity of composition operators
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Karim, Noureddine [1] ; Benchiheb, Otmane [1] ; Amouch, Mohamed [1]
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[1] Department of Mathematics, Faculty of science, Chouaib Doukkali University, El Jadida, Morocco
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- Localización: Collectanea mathematica, ISSN 0010-0757, Vol. 75, Fasc. 1, 2024, págs. 171-187
- Idioma: inglés
- Texto completo no disponible (Saber más ...)
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Resumen
A Furstenberg family \mathcal {F} is a collection of infinite subsets of the set of positive integers such that if A\subset B and A\in \mathcal {F}, then B\in \mathcal {F}. For a Furstenberg family \mathcal {F}, finitely many operators T_1,...,T_N acting on a common topological vector space X are said to be disjoint \mathcal {F}-transitive if for every non-empty open subsets U_0,...,U_N of X the set \{n\in \mathbb {N}:\ U_0 \cap T_1^{-n}(U_1)\cap ...\cap T_N^{-n}(U_N)\ne \emptyset \} belongs to \mathcal {F}. In this paper, depending on the topological properties of \Omega, we characterize the disjoint \mathcal {F}-transitivity of N\ge 2 composition operators C_{\phi _1},\ldots ,C_{\phi _N} acting on the space H(\Omega ) of holomorphic maps on a domain \Omega \subset \mathbb {C} by establishing a necessary and sufficient condition in terms of their symbols \phi _1,...,\phi _N.
