2017/03/27 by Yunied Puig, Puig, Yunied
Mathematics · #Advanced Topics in Algebra #Analytic and geometric function theory #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory
paper · pdf · doi:10.48550/arxiv.1703.09172
openalex publication_date 2017/03/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Motivated by a question posed by Sophie Grivaux concerning the regularity of the orbits of frequently hypercylic operators, we show the following: for any operator T on a separable metrizable and complete topological vector space X which is both frequently hypercyclic and piecewise syndetic hypercyclic, the lower density and upper Banach density of the recurrence set \n≥ 1: Tn x∈ U\ are different, for any hypercyclic vector x∈ X for T, and a certain collection of non-empty open sets U⊆ X. As an immediate consequence we got a sufficient condition for a chaotic operator to be non frequently hypercyclic.