Disjoint strong transitivity of composition operators

• Karim, Noureddine ^[1] ; Benchiheb, Otmane ^[1] ; Amouch, Mohamed ^[1]
  1. [1] Department of Mathematics, Faculty of science, Chouaib Doukkali University, El Jadida, Morocco
• Localización: Collectanea mathematica, ISSN 0010-0757, Vol. 75, Fasc. 1, 2024, págs. 171-187
• Idioma: inglés
• DOI: 10.1007/s13348-022-00383-4
• Texto completo no disponible (Saber más ...)
• 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.

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