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

 

Typical operators admit common cyclic vectors


Author: Pavel Zorin-Kranich
Journal: Proc. Amer. Math. Soc. 141 (2013), 2371-2378
MSC (2010): Primary 47A16
Published electronically: March 14, 2013
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Abstract: Given a countable dense subset $ D$ of an infinite-dimensional separable Hilbert space $ H$, the set of operators for which every vector in $ D$ except zero is hypercyclic (weakly supercyclic) is residual for the strong (resp. weak) operator topology in the unit ball of $ L(H)$ multiplied by $ R>1$ (resp. $ R>0$).


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Additional Information

Pavel Zorin-Kranich
Affiliation: Korteweg de Vries Instituut voor Wiskunde, Universiteit van Amsterdam, P. O. Box 94248, 1090 GE Amsterdam, The Netherlands
Email: zorin-kranich@uva.nl

DOI: http://dx.doi.org/10.1090/S0002-9939-2013-11512-1
PII: S 0002-9939(2013)11512-1
Keywords: Cyclic vector, hypercyclic vector, weakly supercyclic vector, typical operator
Received by editor(s): August 26, 2010
Received by editor(s) in revised form: March 26, 2011, and October 18, 2011
Published electronically: March 14, 2013
Communicated by: Marius Junge
Article copyright: © Copyright 2013 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.