Differentiable vectors and unitary representations of Frechet-Lie supergroups

Hadi Salmasian, Karl-Hermann Neeb

Published 2012-08-13, updated 2012-11-16Version 2

For a locally convex Lie group with the Trotter property, we prove that the space of k-times differentiable vectors of a unitary representation is equal to the intersection of domains of k-fold products of the Lie algebra action. The result also holds for continuous representations of locally exponential groups on metrizable locally convex spaces. As an application, we extend a key stability theorem in the representation theory of Lie supergroups beyond the Banach case.