The Kitai criterion and backward shifts
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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 $T$.References
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Additional Information
- Stanislav Shkarin
- Affiliation: Department of Pure Mathematics, Queen’s University Belfast, University Road, BT7 1NN Belfast, United Kingdom
- Email: s.shkarin@qub.ac.uk
- 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
- © Copyright 2008
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 136 (2008), 1659-1670
- MSC (2000): Primary 47A16, 37A25
- DOI: https://doi.org/10.1090/S0002-9939-08-09179-X
- MathSciNet review: 2373595