Topologically mixing hypercyclic operators. (English) Zbl 1054.47006

Authors’ abstract: “Let \(X\) be a separable Fréchet space. We prove that a linear operator \(T: X\to X\) satisfying a special case of the hypercyclicity criterion is topologically mixing, i.e., for any given open sets \(U\), \(V\) there exists a positive integer \(N\) such that \(T^n(U)\cap V\neq\emptyset\) for any \(n\geq N\). We also characterize those weighted backward shift operators that are topologically mixing.”


47A16 Cyclic vectors, hypercyclic and chaotic operators
47B37 Linear operators on special spaces (weighted shifts, operators on sequence spaces, etc.)
37A25 Ergodicity, mixing, rates of mixing
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