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

 

On subspace-hypercyclic operators


Author: Can Minh Le
Journal: Proc. Amer. Math. Soc. 139 (2011), 2847-2852
MSC (2010): Primary 47A16; Secondary 47B37, 37B99
Published electronically: January 7, 2011
MathSciNet review: 2801626
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Abstract: In this paper we study an operator $ T$ on a Banach space $ E$ which is $ M$-hypercyclic for some subspace $ M$ of $ E$. We give a sufficient condition for such an operator to be $ M$-hypercyclic and use it to answer negatively two questions asked by Madore and Martínez-Avendaño. We also give a sufficient condition for $ T$ to be $ M$-hypercyclic for all finite co-dimensional subspaces $ M$ in $ E$.


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Additional Information

Can Minh Le
Affiliation: Department of Mathematics and Sciences, Kent State University, Kent, Ohio 44242
Email: cle@math.kent.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-2011-10754-8
PII: S 0002-9939(2011)10754-8
Received by editor(s): May 4, 2010
Received by editor(s) in revised form: July 28, 2010
Published electronically: January 7, 2011
Additional Notes: The author would like to express his thanks to Professor Richard M. Aron for his invaluable advice.
Communicated by: Nigel J. Kalton
Article copyright: © Copyright 2011 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.