Projective Analytic Vectors and Infinitesimal Generators

Abstract

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.

20 pages. Final version published in Mathematische Nachrichten. This work investigates in more depth the concept of a projective analytic vector, which has first appeared in arXiv:1906.07931v3. arXiv admin note: text overlap with arXiv:1906.07931

References in corpus (1)

• Exponentiation of Lie Algebras of Linear Operators on Locally Convex Spaces