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Journal of Lie Theory 24 (2014), No. 2, 545--560
Copyright Heldermann Verlag 2014

Regularity in Milnor's Sense for Ascending Unions of Banach-Lie Groups

Rafael Dahmen
Fachbereich Mathematik, Technische Universitšt, Schlossgartenstrasse 7, 64289 Darmstadt, Germany

We give a criterion for the union of an ascending sequence of Banach-Lie 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 Michal-Bastiani (Keller's Cc-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: Banach-Lie group, Baker-Campbell-Hausdorff-series, complex analytic mapping, direct limit, infinite dimensional Lie group, Lie theory, local Lie group, locally convex vector space, non-linear functional analysis, regular Lie group.

MSC: 58B25, 22E65

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