Upper frequent hypercyclicity and related notions

Upper frequent hypercyclicity and related notions

Enhancing a recent result of Bayart and Ruzsa we obtain a Birkhoff-type characterization of upper frequently hypercyclic operators and a corresponding Upper Frequent Hypercyclicity Criterion. As an application we characterize upper frequently hypercyclic weighted backward shifts on sequence spaces,...

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Veröffentlicht in:Revista matemática complutense 2018-09, Vol.31 (3), p.673-711
Hauptverfasser: Bonilla, Antonio, Grosse-Erdmann, Karl-G.
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Algebra
Analysis
Applications of Mathematics
Geometry
Mathematics
Mathematics and Statistics
Operators
Topology
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Grosse-Erdmann, Karl-G.
description Enhancing a recent result of Bayart and Ruzsa we obtain a Birkhoff-type characterization of upper frequently hypercyclic operators and a corresponding Upper Frequent Hypercyclicity Criterion. As an application we characterize upper frequently hypercyclic weighted backward shifts on sequence spaces, which in turn allows us to come up with various counter-examples in linear dynamics that are substantially simpler than those previously obtained in the literature. More generally, we introduce the notion of upper Furstenberg families A and show that our main results hold for the corresponding A -hypercyclic operators.
doi_str_mv 10.1007/s13163-018-0260-y
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source Universidad Complutense de Madrid Free Journals; SpringerLink Journals - AutoHoldings
subjects Algebra
Analysis
Applications of Mathematics
Geometry
Mathematics
Mathematics and Statistics
Operators
Topology
title Upper frequent hypercyclicity and related notions
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