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
MathSciNet review: 3043018
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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$).

References [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2010): 47A16

Retrieve articles in all journals with MSC (2010): 47A16

Additional Information

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

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.