On the exponential stability and dichotomy of $C_0$-semigroups
Volume 132 / 1999
Studia Mathematica 132 (1999), 141-149
DOI: 10.4064/sm-132-2-141-149
Abstract
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.
