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The Kitai criterion and backward shifts
Author(s):
Stanislav
Shkarin
Journal:
Proc. Amer. Math. Soc.
136
(2008),
1659-1670.
MSC (2000):
Primary 47A16, 37A25
Posted:
January 17, 2008
MathSciNet review:
2373595
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Abstract:
It is proved that for any separable infinite dimensional Banach space  , there is a bounded linear operator  on  such that  satisfies the Kitai criterion. The proof is based on a quasisimilarity argument and on showing that  satisfies the Kitai criterion for certain backward weighted shifts  .
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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
DOI:
10.1090/S0002-9939-08-09179-X
PII:
S 0002-9939(08)09179-X
Keywords:
Hypercyclic operators,
mixing operators,
the Kitai criterion,
biorthogonal sequences,
backward shifts,
quasisimilarity
Received by editor(s):
November 9, 2006
Posted:
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 of article:
Copyright
2008,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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