### On the exponential stability and dichotomy of ${C}_{0}$-semigroups

Phóng Vũ (1999)

Studia Mathematica

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A characterization of exponentially dichotomic and exponentially stable ${C}_{0}$-semigroups in terms of solutions of an operator equation of Lyapunov type is presented. As a corollary a new and shorter proof of van Neerven’s recent characterization of exponential stability in terms of boundedness of convolutions of a semigroup with almost periodic functions is given.