Abstract
Based on our preceding paper, this note is concerned with the exponential stability of the solution semigroup for the abstract linear autonomous functional differential equation urn:x-wiley:01611712:media:ijmm549151:ijmm549151-math-0001 where L is a continuous linear operator on some abstract phase space B into a Banach space E. We prove that the solution semigroup of (∗) is exponentially stable if and only if the fundamental operator (∗) is exponentially stable and the phase space B is an exponentially fading memory space.
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