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The Kitai criterion and backward shifts

Author: Stanislav Shkarin
Journal: Proc. Amer. Math. Soc. 136 (2008), 1659-1670
MSC (2000): Primary 47A16, 37A25
Published electronically: January 17, 2008
MathSciNet review: 2373595
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Abstract: It is proved that for any separable infinite dimensional Banach space $ X$, there is a bounded linear operator $ T$ on $ X$ such that $ T$ satisfies the Kitai criterion. The proof is based on a quasisimilarity argument and on showing that $ I+T$ satisfies the Kitai criterion for certain backward weighted shifts $ T$.

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Additional Information

Stanislav Shkarin
Affiliation: Department of Pure Mathematics, Queen’s University Belfast, University Road, BT7 1NN Belfast, United Kingdom

Keywords: Hypercyclic operators, mixing operators, the Kitai criterion, biorthogonal sequences, backward shifts, quasisimilarity
Received by editor(s): November 9, 2006
Published electronically: January 17, 2008
Additional Notes: The author was partially supported by Plan Nacional I+D+I grant no. MTM2006-09060, Junta de Andalucía FQM-260 and British Engineering and Physical Research Council Grant GR/T25552/01.
Communicated by: Jonathan M. Borwein
Article copyright: © Copyright 2008 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.