Projective analytic vectors and infinitesimal generators

Abstract

AbstractWe 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.