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A characterization of exponential stability for periodic evolution families in terms of lower semicontinuous functionals. (English) Zbl 1089.47031
In the present paper, the author investigates the exponential stability of 1-periodic evolution families in a Banach space. He uses lower semicontinuous functionals to give a characterisation of exponential stability and extends J. van Neerven’s result [Integral Equations Oper. Theory, 4, 482–492 (2002; Zbl 1040.47033)] to 1-periodic evolution families of bounded linear operators.
MSC:
47D03 Groups and semigroups of linear operators
47A10 Spectrum, resolvent
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