Frequently hypercyclic operators with irregularly visiting orbits
| Autor: | Sophie Grivaux |
|---|---|
| Přispěvatelé: | Centre National de la Recherche Scientifique (CNRS), Laboratoire Paul Painlevé - UMR 8524 (LPP), Université de Lille-Centre National de la Recherche Scientifique (CNRS), Laboratoire Paul Painlevé (LPP), ANR-17-CE40-0021,FRONT2017,Frontières de la théorie des opérateurs(2017) |
| Jazyk: | angličtina |
| Rok vydání: | 2018 |
| Předmět: |
Applied Mathematics
010102 general mathematics Open set Banach space Dynamical Systems (math.DS) [MATH.MATH-FA]Mathematics [math]/Functional Analysis [math.FA] 01 natural sciences Functional Analysis (math.FA) Bounded operator Separable space Mathematics - Functional Analysis Combinatorics Operator (computer programming) 0103 physical sciences FOS: Mathematics 010307 mathematical physics Mathematics - Dynamical Systems 0101 mathematics Analysis Mathematics |
| Zdroj: | Journal of Mathematical Analysis and Applications Journal of Mathematical Analysis and Applications, Elsevier, 2018, 462 (1), pp.542-553. ⟨10.1016/j.jmaa.2018.02.020⟩ Journal of Mathematical Analysis and Applications, 2018, 462 (1), pp.542-553. ⟨10.1016/j.jmaa.2018.02.020⟩ |
| ISSN: | 0022-247X 1096-0813 |
| DOI: | 10.1016/j.jmaa.2018.02.020⟩ |
| Popis: | We prove that a bounded operator $T$ on a separable Banach space $X$ satisfying a strong form of the Frequent Hypercyclicity Criterion (which implies in particular that the operator is universal in the sense of Glasner and Weiss) admits frequently hypercyclic vectors with irregularly visiting orbits, i.e. vectors $x\in X$ such that the set $\mathcal{N}_T(x,U)=\{n\ge 1\,;\,T^{n}x\in U\}$ of return times of $x$ into $U$ under the action of $T$ has positive lower density for every non-empty open set $U\subseteq X$, but there exists a non-empty open set $U_0\subseteq X$ such that $\nt{x}{U_0}$ has no density. Change of title, following referee's suggestion |
| Databáze: | OpenAIRE |
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