On the exponential stability and dichotomy of $C_0$-semigroups

Volume 132 / 1999

Vũ Quôc Phóng Studia Mathematica 132 (1999), 141-149 DOI: 10.4064/sm-132-2-141-149


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.


  • Vũ Quôc Phóng

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