The Hypercyclicity Criterion for sequences of operators

• Autorzy: L. Bernal-González , K.-G. Grosse-Erdmann
• Języki publikacji: EN

Abstrakty

EN

We show that under no hypotheses on the density of the ranges of the mappings involved, an almost-commuting sequence (Tₙ) of operators on an F-space X satisfies the Hypercyclicity Criterion if and only if it has a hereditarily hypercyclic subsequence $(T_{n_{k}})$, and if and only if the sequence (Tₙ ⊕ Tₙ) is hypercyclic on X × X. This strengthens and extends a recent result due to Bès and Peris. We also find a new characterization of the Hypercyclicity Criterion in terms of a condition introduced by Godefroy and Shapiro. Finally, we show that a weakly commuting hypercyclic sequence (Tₙ) satisfies the Hypercyclicity Criterion whenever it has a dense set of points with precompact orbits. We remark that some of our results are new even in the case of iterates (Tⁿ) of a single operator T.

Kategorie tematyczne

• 54H20: Topological dynamics
• 47A16: Cyclic vectors, hypercyclic and chaotic operators
• 46A16: Not locally convex spaces (metrizable topological linear spaces, locally bounded spaces, quasi-Banach spaces, etc.)
• 47B33: Composition operators

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2003
• Tom: 157
• Numer: 1
• Strony: 17-32

Daty

wydano

2003

Twórcy

autor

L. Bernal-González

• Departamento de Análisis Matemático, Facultad de Matemáticas, Apdo. 1160, Universidad de Sevilla, Avda. Reina Mercedes, 41080 Sevilla, Spain

autor

K.-G. Grosse-Erdmann

• Fachbereich Mathematik, Fern Universität Hagen, D-58084 Hagen, Germany

Identyfikatory

DOI

10.4064/sm157-1-2