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

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.

Keywords

• strongly (weakly) almost periodic function
• sequentially weakly complete Banach space
• densely defined linear operator
• dual operator
• Hilbert space
• nonnegative self-adjoint operator.