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.
DOI: http://dx.doi.org/10.7900/jot.2013mar11.2001
Keywords: linear dynamics, frequently hypercyclic operators,
spectrum of operators, entire functions of exponential type
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