**Yuri Latushkin and Stephen Montgomery-Smith, Lyapunov theorems for Banach spaces.**
*Bull. Amer. Math. Soc. (N.S.) ***31** (1994) 44-49.
We present a spectral mapping theorem for semigroups on any Banach space \(E\). From this, we obtain a characterization of exponential dichotomy for nonautonomous differential equations for \(E\)-valued functions. This characterization is given in terms of the spectrum of the generator of the semigroup of evolutionary operators.
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