Operators with eigenvalues and extreme cases of stability
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- by Larry Downey and Per Enflo PDF
- Proc. Amer. Math. Soc. 132 (2004), 719-724 Request permission
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.References
- P. Erdös and T. Grünwald, On polynomials with only real roots, Ann. of Math. (2) 40 (1939), 537–548. MR 7, DOI 10.2307/1968938
- C. J. Everett Jr., Annihilator ideals and representation iteration for abstract rings, Duke Math. J. 5 (1939), 623–627. MR 13
- Bernard Beauzamy, Introduction to operator theory and invariant subspaces, North-Holland Mathematical Library, vol. 42, North-Holland Publishing Co., Amsterdam, 1988. MR 967989
- Tosio Kato, Perturbation theory for linear operators, Die Grundlehren der mathematischen Wissenschaften, Band 132, Springer-Verlag New York, Inc., New York, 1966. MR 0203473
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
- 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
- © Copyright 2003 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 132 (2004), 719-724
- MSC (2000): Primary 47A55, 47A10
- DOI: https://doi.org/10.1090/S0002-9939-03-07059-X
- MathSciNet review: 2019948