Fast orbital convergence reveals more hypercyclic vectors

• Moothathu, T. K. Subrahmonian ^[1]
  1. [1] University of Hyderabad

     University of Hyderabad

     India

     
• Localización: Applied general topology, ISSN-e 1989-4147, ISSN 1576-9402, Vol. 26, Nº. 2, 2025, págs. 593-600
• Idioma: inglés
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• Resumen

  • Let X be an infinite dimensional separable Banach space, T : X → X be a hypercyclic operator, and x ∈ X be a (frequently) hypercyclic vector of T. We show that if the terms from the T-orbit of x converge to a vector y sufficiently fast, then y is also a hypercyclic vector of T. As a corollary, we deduce that if T is a frequently hypercyclic operator with spectral radius r(T) = 1, then lim_{n\to \infty} ∥Tnx∥^{1/n} = 1 for every frequently hypercyclic vector x of T. Some related observations are also made.