Proceedings of the American Mathematical Society

			Journals Home Search Author Info Subscribe Tech Support My Subscriptions Help
ISSN 1088-6826(e) ISSN 0002-9939(p)

Operators with eigenvalues and extreme cases of stability

Author(s): Larry Downey; Per Enflo
Journal: Proc. Amer. Math. Soc. 132 (2004), 719-724.
MSC (2000): Primary 47A55, 47A10
Posted: October 15, 2003
MathSciNet review: 2019948
Retrieve article in: PDF
This article is available free of charge

Abstract | References | Similar articles | Additional information

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 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:

1.: Dieudonné, J., Sur les homomorphismes d'espaces normés, Bull. Sci. Math., Vol. 67, (1943), 72-84. MR 7:124c
2.: Atkinson, F. V., The Normal Solubility of Linear Equations in Normed Spaces, Mat. Sbornik, Vol. 28, (1951), 3-14. MR 13:46d
3.: Beauzamy, B., Introduction to Operator Theory and Invariant Subspaces, North-Holland Publishing Co., Amsterdam, 1988. MR 90d:47001
4.: Kato, T., Perturbation Theory for Linear Operators, Die Grundlehren der mathematischen Wissenschaften, Band 132, Springer-Verlag, New York, 1966. MR 34:3324

	Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
\|