Lyapunov theorems for Banach spaces

Authors:
Yu. Latushkin and S. Montgomery-Smith

Journal:
Bull. Amer. Math. Soc. **31** (1994), 44-49

MSC:
Primary 47D06; Secondary 34D05, 34D20, 34G10, 47N20

DOI:
https://doi.org/10.1090/S0273-0979-1994-00495-1

MathSciNet review:
1249356

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Abstract | References | Similar Articles | Additional Information

Abstract: 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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Additional Information

DOI:
https://doi.org/10.1090/S0273-0979-1994-00495-1

Keywords:
Hyperbolicity,
evolution family,
exponential dichotomy,
weighted composition operators,
spectral mapping theorem

Article copyright:
© Copyright 1994
American Mathematical Society