Dynamics of shift operators on non-metrizable sequence spaces

  • José Bonet

    Universitat Politècnica de València, Spain
  • Thomas Kalmes

    Technische Universität Chemnitz, Germany
  • Alfredo Peris

    Universidad Politècnia de València, Spain
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Abstract

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 in terms of the defining sequence of weights . We further discuss several examples and show that the annihilation operator from quantum mechanics is mixing, sequentially hypercyclic, chaotic, and topologically ergodic on .

Cite this article

José Bonet, Thomas Kalmes, Alfredo Peris, Dynamics of shift operators on non-metrizable sequence spaces. Rev. Mat. Iberoam. 37 (2021), no. 6, pp. 2373–2397

DOI 10.4171/RMI/1267