ABSTRACT
Let W and V be real separable Hilbert spaces, satisfying W c-► V, where by we mean that W C V and the canonical injection W —* V, x »—► x is continuous and W is dense in V. We consider Co-semigroups S(-) on V which restrict to Co-semigroups on W. The infinitesimal generators of 5( ) on V and W will be denoted by A v and A w respectively. The following definition can be found in [22] and [2]. It was first stated in [22], but we use the formulation of [2].
