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• # Artykuł - szczegóły

## Studia Mathematica

2003 | 157 | 1 | 17-32

## The Hypercyclicity Criterion for sequences of operators

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.

17-32

wydano
2003

### Twórcy

autor
• Departamento de Análisis Matemático, Facultad de Matemáticas, Apdo. 1160, Universidad de Sevilla, Avda. Reina Mercedes, 41080 Sevilla, Spain
autor
• Fachbereich Mathematik, Fern Universität Hagen, D-58084 Hagen, Germany