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Operator approximations with stable elgenvalues

Part of: Approximations and expansions Special classes of linear operators General theory of linear operators

Published online by Cambridge University Press:  09 April 2009

Richard Bouldin
Richard Bouldin
Affiliation:
Department of MathematicsUniversity of Georgia Athens, Georgia 30602, U.S.A.
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Abstract

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Suppose λ is an isolated eigenvalue of the (bounded linear) operator T on the Banach space X and the algebraic multiplicity of λ is finite. Let Tn be a sequence of operators on X that converge to T pointwise, that is, Tnx → Tx for every x ∈ X. If ‖(T − Tn)Tn‖ and ‖Tn(T − Tn)‖ converge to 0 then Tn is strongly stable at λ.

Keywords

eigenvalueisolated eigenvaluestablestrongly stableoperator approximationstrong convergenceToeplitz operator

MSC classification

Secondary: 47A99: None of the above, but in this section 47B35: Toeplitz operators, Hankel operators, Wiener-Hopf operators 41A35: Approximation by operators (in particular, by integral operators)
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 49 , Issue 2 , October 1990 , pp. 250 - 257
Copyright
Copyright © Australian Mathematical Society 1990

References

[1]Ahues, M., ‘A class of strongly stable operator approximations,’ J. Austral. Math. Soc. Ser. B 28 (1987), 435–442.CrossRefGoogle Scholar
[2]Anselone, P. M., Collectively compact operator approximation theory, (Prentice-Hall, Englewood Cliffs, N. J., 1971).Google Scholar
[3]Chatelin, F., Spectral approximation of linear operators, (Academic Press, New York, 1983).Google Scholar
[4]Dunford, N. and Schwartz, J. T., Linear operators, Vol. 1, (John Wiley, New York, 1964).Google Scholar
[5]Halmos, P. R., A Hilbert space problem book, (Van Nostrand, Princeton, N. J., 1967).Google Scholar
[6]Kato, T., Perturbation theory for linear operators, (Springer-Verlag, New York, 1966).Google Scholar