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Epsilon-hypercyclic operators on a Hilbert space
Author(s):
Frédéric
Bayart
Journal:
Proc. Amer. Math. Soc.
138
(2010),
4037-4043.
MSC (2010):
Primary 47A16, 47B37
Posted:
May 17, 2010
MathSciNet review:
2679624
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Abstract:
For every fixed  , we construct a bounded linear operator on the separable Hilbert space having an orbit which intersects every cone of aperture  , but such that every orbit avoids a certain ball of positive radius (which depends on the orbit) and a fixed centre.
References:
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Epsilon-hypercyclic operators.
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- P. S. Bourdon and N. S. Feldman.
Somewhere dense orbits are everywhere dense.
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A weakly hypercyclic operator that is not norm hypercyclic.
J. Operator Theory, 52:39-59, 2004. MR 2091459 (2005e:47017) - 5.
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Perturbations of hypercyclic vectors.
J. Math. Anal. Appl., 273:67-74, 2002. MR 1933016 (2003h:47012) - 6.
- S. Shkarin.
Non-sequential weak supercyclicity and hypercyclicity.
J. Funct. Anal., 242:37-77, 2007. MR 2274015 (2007i:47010)
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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:
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
Posted:
May 17, 2010
Communicated by:
Nigel J. Kalton
Copyright of article:
Copyright
2010,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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