Topologically mixing hypercyclic operators

Abstract

Let X X be a separable Fréchet space. We prove that a linear operator T : X → X T:X\to X satisfying a special case of the Hypercyclicity Criterion is topologically mixing, i.e. for any given open sets U , V U,V there exists a positive integer N N such that T n ( U ) ∩ V ≠ ∅ T^n(U)\cap V\neq \emptyset for any n ≥ N . n\ge N. We also characterize those weighted backward shift operators that are topologically mixing.