Lyapunov theorems for Banach spaces

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.

6 pages

References in corpus (1)

• Evolutionary Semigroups and Lyapunov Theorems in Banach Spaces

Cited by in corpus (3)

• Harmonic and Spectral Analysis of Abstract Parabolic Operators in Homogeneous Function Spaces
• Generalized evolution semigroups and general dichotomies
• Stability and Dichotomy of Positive Semigroups on $L_p$