Journal of Lie Theory 30 (2020), No. 1, 025--032
Copyright Heldermann Verlag 2020
The Strong Trotter Property for Locally μ-Convex Lie Groups
Fakultät für Mathematik und Informatik, Universität Würzburg, Würzburg, Germany
We show that an infinite dimensional Lie group in Milnor's sense has the strong Trotter property if it is locally μ-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 C0-continuity of the evolution map on its domain. In particular, the result proven in this paper significantly extends the respective result obtained by Glöckner in the context of measurable regularity.
Keywords: Infinite-dimensional Lie groups, Trotter property.
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