
Journal of Lie Theory 24 (2014), No. 2, 545560 Copyright Heldermann Verlag 2014 Regularity in Milnor's Sense for Ascending Unions of BanachLie Groups Rafael Dahmen Fachbereich Mathematik, Technische Universität, Schlossgartenstrasse 7, 64289 Darmstadt, Germany dahmen@mathematik.tudarmstadt.de We give a criterion for the union of an ascending sequence of BanachLie groups to be a regular Lie group in Milnor's sense. It was shown in earlier work that this union carries a Lie group structure. We use the differential calculus by MichalBastiani (Keller's C_{c}^{∞}calculus). In a future article we will show, using similar techniques, that groups of germs of local diffeomorphisms are regular, thus solving an open problem posed by K.H. Neeb. Keywords: BanachLie group, BakerCampbellHausdorffseries, complex analytic mapping, direct limit, infinite dimensional Lie group, Lie theory, local Lie group, locally convex vector space, nonlinear functional analysis, regular Lie group. MSC: 58B25, 22E65 [ Fulltextpdf (319 KB)] for subscribers only. 