Lyapunov operator inequalities for exponential stability of Banach space semigroups of operators

@article{Preda2012LyapunovOI,
  title={Lyapunov operator inequalities for exponential stability of Banach space semigroups of operators},
  author={Ciprian Preda and Petre Preda},
  journal={Appl. Math. Lett.},
  year={2012},
  volume={25},
  pages={401-403}
}
We obtain continuous-time and discrete-time Lyapunov operator inequalities for the exponential stability of strongly continuous, one-parameter semigroups acting on Banach spaces. Thus we extend the classic result of Datko (1970) [2] from Hilbert spaces to Banach spaces. © 2011 Elsevier Ltd. All rights reserved.