摘要
For a sequence {T n } of continuous linear operators on a separable Fréhet space X, we discuss necessary conditions and sufficient conditions for {T n } to be topologically mixing, and the relations between topological mixing and the Hypercyclicity Criterion. Among them are: 1) topological mixing is equivalent to being hereditarily densely hypercyclic; 2) the Hypercyclicity Criterion with respect to the full sequence N implies topological mixing; 3) topological mixing implies the Hypercyclicity Criterion with respect to some sequence {n k ⊂ ℕot be syndetic in general, and also implies condition (b) of the Hypercyclicity Criterion with respect to the full sequence. Applications to two examples of operators on the Fréhet space H(ℂ) of entire functions are also discussed. © 2006 American Mathematical Society.