The Strong Trotter Property for Locally μ-Convex Lie Groups

We show that an infinite dimensional Lie group in Milnor's sense has the strong Trotter property if it is locally mu-convex. This is a continuity condition imposed on the Lie group multiplication that generalizes the triangle inequality for locally convex vector spaces, and is equivalent to C-0-continuity of the evolution map on its domain. In particular, the result proven in this paper significantly extends the respective result obtained by Glockner in the context of measurable regularity.