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Journal of Operator Theory

Volume 72, Issue 2, Fall 2014  pp. 329-342.

On the intersection of the spectrum of frequently hypercyclic operators with the unit circle

Authors:  Hans-Peter Beise
Author institution: Fachbereich IV, University of Trier, Trier, 54286, Germany

Summary:  We exclude the existence of frequently hypercyclic operators that have a spectrum contained in the closed unit disc and that intersects the unit circle in only finitely many points under certain additional conditions. This extends a result of S. Shkarin, which states that the spectrum of a frequently hypercyclic operator cannot have isolated points.

Keywords:  linear dynamics, frequently hypercyclic operators, spectrum of operators, entire functions of exponential type

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