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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.”

MSC:

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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