Exponential dichotomy and strongly stable vectors of Hilbert space contraction semigroups

摘要

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 asso ciated with the semigroup. Necessary and su.cient conditions for exponential stability and non-exponential stability are investigated in terms of norm inequalities—instead of a Lyapunov operator equation.