Recurrence for weighted pseudo-shift operators

• Mohamed Amouch ^[1] ; Fatima-ezzahra Sadek ^[1]
  1. [1] Department of Mathematics, Chouaib Doukkali University, Faculty of Sciences, El Jadida, Morocco
• Localización: Revista de la Unión Matemática Argentina, ISSN 0041-6932, ISSN-e 1669-9637, Vol. 68, Nº. 2, 2025, págs. 775-786
• Idioma: inglés
• DOI: 10.33044/revuma.4120
• Enlaces
  • Texto completo
• Resumen

  • We provide a characterization of multiply recurrent operators that act on a Fr´echet space. As an application, we extend the weighted shift results established by Costakis and Parissis (2012). We achieve this by characterizing topologically multiply recurrent pseudo-shifts acting on an F-sequence space indexed by an arbitrary countable infinite set. This characterization is in terms of the weights, the OP-basis and the shift mapping. Additionally, we establish that the recurrence and the hypercyclicity of pseudo-shifts are equivalent.

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