Lyapunov theorems for Banach spaces

Details Lyapunov theorems for Banach spaces Lyapunov theorems for Banach spaces

1993-02-24

arxiv.org/abs/math/9302216v1

Bull. Amer. Math. Soc. (N.S.) 31 (1994) 44-49

Mathematics

Functional Analysis

6 pages

Scientific paper

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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