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On strongly stable approximations

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

Published online by Cambridge University Press:  09 April 2009

M. Thamban Nair
M. Thamban Nair
Affiliation:
Goa UniversityGoa-403 202, India
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Abstract

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Ahues (1987) and Bouldin (1990) have given sufficient conditions for the strong stability of a sequence (Tn) of operators at an isolated eigenvalue of an operator T. This paper provides a unified treatment of their results and also generalizes so as to facilitate their application to a broad class of operators.

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 52 , Issue 2 , April 1992 , pp. 251 - 260
Copyright
Copyright © Australian Mathematical Society 1992

References

[1]Ahues, M., A class of strongly stable operator approximations, J. Au.st. Math. Soc. Ser B 28 (1987), 435–442.CrossRefGoogle Scholar
[2]Anselone, P. M., Collectively Compact Operator Approximation Theory (Prentice-Hall, Englewood, Cliffs, New Jersey, 1971).Google Scholar
[3]Bouldin, R., Operator approximations with stable eigenvalues, J. Aust. Math. Soc. Ser A, 49 (1990), 250–257.CrossRefGoogle Scholar
[4]Chatelin, F., Spectral approximation of Linear Operators (Academic Press, New York, 1983).Google Scholar
[5]Kato, T., Perturbation Theory for Linear Operators (Springer-Verlag, Berlin/Heidelberg/ New York, 1976).Google Scholar