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

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Abstract | References | Similar Articles | Additional Information

Abstract: Given a countable dense subset of an infinite-dimensional separable Hilbert space , the set of operators for which every vector in except zero is hypercyclic (weakly supercyclic) is residual for the strong (resp. weak) operator topology in the unit ball of multiplied by (resp. ).

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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:
https://doi.org/10.1090/S0002-9939-2013-11512-1

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.