Frequently recurrent operators

Motivated by a recent investigation of Costakis et al. on the notion of recurrence in linear dynamics, we study various stronger forms of recurrence for linear operators, in particular that of frequent recurrence. We study, among other things, the relationship between a type of recurrence and the co...

Full description

Saved in:
Bibliographic Details
Published in:Journal of functional analysis 2022-12, Vol.283 (12), p.109713, Article 109713
Main Authors: Bonilla, Antonio, Grosse-Erdmann, Karl-G., López-Martínez, Antoni, Peris, Alfred
Format: Article
Language:English
Subjects:
Frequently hypercyclic operators
Furstenberg families
Hypercyclic operators
Recurrence
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:Motivated by a recent investigation of Costakis et al. on the notion of recurrence in linear dynamics, we study various stronger forms of recurrence for linear operators, in particular that of frequent recurrence. We study, among other things, the relationship between a type of recurrence and the corresponding notion of hypercyclicity, the influence of power boundedness, and the interplay between recurrence and spectral properties. We obtain, in particular, Ansari- and Léon-Müller-type theorems for F-recurrence under very weak assumptions on the Furstenberg family F. This allows us, as a by-product, to deduce Ansari- and Léon-Müller-type theorems for F-hypercyclicity.
ISSN:0022-1236
1096-0783
DOI:10.1016/j.jfa.2022.109713