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

 

Operators with eigenvalues and extreme cases of stability


Authors: Larry Downey and Per Enflo
Journal: Proc. Amer. Math. Soc. 132 (2004), 719-724
MSC (2000): Primary 47A55, 47A10
Published electronically: October 15, 2003
MathSciNet review: 2019948
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Abstract: In the following, we consider some cases where the point spectrum of an operator is either very stable or very unstable with respect to small perturbations of the operator. The main result is about the shift operator on $l_2,$ whose point spectrum is what we will call strongly stable. We also give some general perturbation results, including a result about the size of the set of operators that have an eigenvalue.


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Additional Information

Larry Downey
Affiliation: School of Science, Penn State University at Erie, Station Road, Erie, Pennsylvania 16563
Email: lmd108@psu.edu

Per Enflo
Affiliation: Department of Mathematics, Kent State University, Kent, Ohio 44240
Email: enflo@math.kent.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-03-07059-X
PII: S 0002-9939(03)07059-X
Keywords: Eigenvalues, operator, stability, strongly stable, shift operator
Received by editor(s): November 9, 2001
Received by editor(s) in revised form: September 13, 2002
Published electronically: October 15, 2003
Communicated by: N. Tomczak-Jaegermann
Article copyright: © Copyright 2003 American Mathematical Society