Difference sets and frequently hypercyclic weighted shifts
نویسندگان
چکیده
We solve several problems on frequently hypercyclic operators. Firstly, we characterize frequently hypercyclic weighted shifts on l(Z), p ≥ 1. Our method uses properties of the difference set of a set with positive upper density. Secondly, we show that there exists an operator which is U-frequently hypercyclic, yet not frequently hypercyclic and that there exists an operator which is frequently hypercyclic, yet not distributionally chaotic. These (surprizing) counterexamples are given by weighted shifts on c0. The construction of these shifts lies on the construction of sets of positive integers whose difference sets have very specific properties.
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تاریخ انتشار 2013