Perturbations of Hypercyclic Vectors

  • NATHAN S. FELDMAN
  • Published 2002

Abstract

We show that a linear operator can have an orbit that comes within a bounded distance of every point, yet is not dense. We also prove that such an operator must be hypercyclic. This gives a more general form of the hypercyclicity criterion. We also show that a sufficiently small perturbation of a hypercyclic vector is still hypercyclic. 

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