Dynamical Properties of Perturbed Weighted Shifts
Ali Messaoudi, José Luiz Tofanin Neto, Ioannis Tsokanos
Abstract
In this paper, sufficient conditions are established for diagonal perturbations of weighted shifts to be supercyclic, hypercyclic, and frequently hypercyclic, extending several classical results for weighted shifts to this more general setting. In addition, a complete analytic characterization of the shadowing property for these operators is obtained. Consequently, examples of frequently hypercyclic perturbed weighted shifts with the shadowing property are constructed.
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