  We establish the notion of a ``projective analytic vector'', whose defining
requirements are weaker than the usual ones of an analytic vector, and use it
to prove generation theorems for one-parameter groups on locally convex spaces.
More specifically, we give a characterization of the generators of strongly
continuous one-parameter groups which arise as the result of a projective limit
procedure, in which the existence of a dense set of projective analytic vectors
plays a central role. An application to strongly continuous Lie group
representations on Banach spaces is given, with a focused analysis on concrete
algebras of functions and of pseudodifferential operators.
