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

 

Linear operators with wild dynamics


Author: Jean-Matthieu Augé
Journal: Proc. Amer. Math. Soc. 140 (2012), 2103-2116
MSC (2010): Primary 47A05; Secondary 47A15, 47A16
Published electronically: October 20, 2011
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Abstract: If $ X$ is a separable infinite-dimensional Banach space, we construct a bounded and linear operator $ R$ on $ X$ such that

$\displaystyle A_R=\{x \in X, \Vert R^tx\Vert \rightarrow \infty \} $

is not dense and has a non-empty interior with the additional property that $ R$ can be written $ I+K$, where $ I$ is the identity and $ K$ is a compact operator. This answers two recent questions of Hájek and Smith.

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Additional Information

Jean-Matthieu Augé
Affiliation: Department of Mathematics, Université Bordeaux 1, 351, cours de la Libération, F-33405 Talence cedex, France
Email: jean-matthieu.auge@math.u-bordeaux1.fr

DOI: http://dx.doi.org/10.1090/S0002-9939-2011-11082-7
PII: S 0002-9939(2011)11082-7
Keywords: Orbits of operators, compact operators
Received by editor(s): November 18, 2010
Received by editor(s) in revised form: February 11, 2011
Published electronically: October 20, 2011
Communicated by: Thomas Schlumprecht
Article copyright: © Copyright 2011 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.