On asymptotic stability of linear time-varying infinite-dimensional systems (Q1062951)

The author proceeds in his study of stability for linear infinite dimensional discrete-time systems (including by a natural discretization retarded functional differential equations). For collectively compact systems asymptotic equistability is shown to be equivalent to uniform (w.r.t. the initial value) asymptotic equistability. Time-varying retarded functional differential equations are collectively compact if the operators at the right hand side have uniformly bounded norms.