Dynamics of shift operators on non-metrizable sequence spaces

• José Bonet ^[1] ; Thomas Kalmes ^[2] ; Alfredo Peris ^[3]
  1. [1] Universidad Politécnica de Valencia

     Universidad Politécnica de Valencia

     Valencia, España

     
  2. [2] Chemnitz University of Technology

     Chemnitz University of Technology

     Kreisfreie Stadt Chemnitz, Alemania

     
  3. [3] Universidad Politècnia de València

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• Localización: Revista matemática iberoamericana, ISSN 0213-2230, Vol. 37, Nº 6, 2021, págs. 2373-2397
• Idioma: inglés
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• Resumen

  • We investigate dynamical properties such as topological transitivity, (sequential) hypercyclicity, and chaos for backward shift operators associated to a Schauder basis on LF-spaces. As an application, we characterize these dynamical properties for weighted generalized backward shifts on Köthe coechelon sequence spaces kp((v(m))m∈N) in terms of the defining sequence of weights (v(m))m∈N. We further discuss several examples and show that the annihilation operator from quantum mechanics is mixing, sequentially hypercyclic, chaotic, and topologically ergodic on S′(R).