International Journal of Mathematics and Mathematical Sciences
Volume 8 (1985), Issue 1, Pages 109-112
doi:10.1155/S0161171285000096
On the spectrum of weakly almost periodic solutions of certain abstract differential equations
Aribindi Satyanarayan Rao1
and L.S. Dube2
1Department of Mathematics, Sir George Williams Campus, Concordia University, Montreal, Quebec, Canada
2Department of Mathematics, Vanier College, 821 Ste-Mis Croix Blvd., St.-Laurent H4L 3x9, Quebec, Canada
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.