Authors introduce δ-topological transitivity, δ-mixing, and a δ-Hypercyclicity Criterion in separable F-spaces, prove UFB-δ-TM implies δ-TM implies δ-TT and that the classical Hypercyclicity Criterion implies the δ-criterion for every δ>0, and verify it for weighted backward shifts.
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A Metric Framework for Approximate Transitivity, Mixing, and Hypercyclicity
Authors introduce δ-topological transitivity, δ-mixing, and a δ-Hypercyclicity Criterion in separable F-spaces, prove UFB-δ-TM implies δ-TM implies δ-TT and that the classical Hypercyclicity Criterion implies the δ-criterion for every δ>0, and verify it for weighted backward shifts.