Abstract

The paper deals with exponential dichotomy and its relationship with strongly stable vectors associated with Hilbert space semigroups. Contraction semigroups are decomposed by using the strongly stability operator associated with the semigroup. Necessary and sufficient conditions for exponential stability and non-exponential stability are investigated in terms of norm inequalities---instead of a Lyapunov operator equation.

Keywords: Exponential stability; strong stability; exponential dichotomy; strong dichotomy

MSC: 47D03, 47A45

Pages:  166--177     

Volume  65 ,  Issue  2 ,  2013