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On the Perron problem for the exponential dichotomy of \(C_0\)-semigroups. (English) Zbl 1097.34532

It is shown that a \(C_0\)-semigroup \(\{T(t)\}_{t\geq 0}\) on a Banach space has an exponential dichotomy when it satisfies a Perron condition. The invertibility of the dichotomic projection is not required.

MSC:

34D09 Dichotomy, trichotomy of solutions to ordinary differential equations
34D05 Asymptotic properties of solutions to ordinary differential equations
34G10 Linear differential equations in abstract spaces
47D06 One-parameter semigroups and linear evolution equations
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