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International Journal of Mathematics and Mathematical Sciences
Volume 8 (1985), Issue 1, Pages 109-112
http://dx.doi.org/10.1155/S0161171285000096

On the spectrum of weakly almost periodic solutions of certain abstract differential equations

1Department of Mathematics, Sir George Williams Campus, Concordia University, Montreal, Quebec, Canada
2Department of Mathematics, Vanier College, 821 Ste-Mis Croix Blvd., St.-Laurent, Quebec H4L 3x9, Canada

Received 15 October 1984

Copyright © 1985 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

In a sequentially weakly complete Banach space, if the dual operator of a linear operator A satisfies certain conditions, then the spectrum of any weakly almost periodic solution of the differential equation u=Au+f is identical with the spectrum of f except at the origin, where f is a weakly almost periodic function.