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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Epsilon-hypercyclic operators on a Hilbert space


Author: Frédéric Bayart
Journal: Proc. Amer. Math. Soc. 138 (2010), 4037-4043
MSC (2010): Primary 47A16, 47B37
Published electronically: May 17, 2010
MathSciNet review: 2679624
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Abstract: For every fixed $ \varepsilon>0$, we construct a bounded linear operator on the separable Hilbert space having an orbit which intersects every cone of aperture $ \varepsilon>0$, but such that every orbit avoids a certain ball of positive radius (which depends on the orbit) and a fixed centre.


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Additional Information

Frédéric Bayart
Affiliation: Laboratoire de Mathématiques, Université Blaise Pascal, Campus des Cézeaux, F-63177 Aubière Cedex, France
Email: Frederic.Bayart@math.univ-bpclermont.fr

DOI: http://dx.doi.org/10.1090/S0002-9939-2010-10414-8
PII: S 0002-9939(2010)10414-8
Keywords: Hypercyclic operators, operator weighted shifts
Received by editor(s): June 16, 2009
Received by editor(s) in revised form: January 20, 2010
Published electronically: May 17, 2010
Communicated by: Nigel J. Kalton
Article copyright: © Copyright 2010 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.