J Austral Math Soc Ser A 49 pp250--257, 1990.

Operator Approximations with Stable Eigenvalues

Richard Bouldin

(Received 28 July 1989)

Abstract

Suppose l is an isolated eigenvalue of the (bounded linear) operator T on the Banach space X and the algebraic multiplicity of l is finite. Let T_n be a sequence of operators on X that converge to T pointwise, that is, T_nx Ž Tx for every x Î X. If ||(T - T_n)T_n|| and ||T_n(T - T_n)|| converge to 0 then T_n is strongly stable at l.

1980 AMS Subject Classification (1985 Revision): 47A99, 47B35, 41A35

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Authors

Richard Bouldin: Department of Mathematics, University of Georgia, Athens, Georgia 30602, U.S.A.

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Last Modified: Wed Feb 19 10:27:52 2003