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Spectral mapping theorem for an evolution semigroup on a space of vector-valued almost-periodic functions. (English) Zbl 1273.47069
The paper is concerned with a strongly continuous and \(q\)-periodic evolution family \(\{U(t,s)\}_{t\geq s\geq 0}\) on a Banach space \(X\) and the related evolution semigroup on a closed subspace of \(BUC(\mathbb{R},X)\). A result concerning uniform exponential stability, which is similar to a known theorem, is given. Moreover, it is shown that the five statements in the result are equivalent under a further assumption.

MSC:
47D06 One-parameter semigroups and linear evolution equations
47A10 Spectrum, resolvent
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