Generalized Cesàro operators in weighted Banach spaces of analytic functions with sup-norms

• Albanese, Angela A. ^[1] ; Bonet, José ^[2] ; Ricker, Werner J. ^[3]
  1. [1] University of Salento

     University of Salento

     Lecce, Italia

     
  2. [2] Universidad Politécnica de Valencia

     Universidad Politécnica de Valencia

     Valencia, España

     
  3. [3] Catholic University of Eichstätt-Ingolstadt

     Catholic University of Eichstätt-Ingolstadt

     Landkreis Eichstätt, Alemania

     

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• Localización: Collectanea mathematica, ISSN 0010-0757, Vol. 76, Fasc. 2, 2025, págs. 397-416
• Idioma: inglés
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• Resumen

  • An investigation is made of the generalized Cesàro operators C_t, for t\in [0,1], when they act on the space H({{\mathbb {D}}}) of holomorphic functions on the open unit disc {{\mathbb {D}}}, on the Banach space H^\infty of bounded analytic functions and on the weighted Banach spaces H_v^\infty and H_v^0 with their sup-norms. Of particular interest are the continuity, compactness, spectrum and point spectrum of C_t as well as their linear dynamics and mean ergodicity.