Exponential dichotomy and strongly stable vectors of Hilbert space contraction semigroups

Nhan Levan, Carlos S. Kubrusly

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.