Journal Home Page

Cumulative Index

List of all Volumes

Complete Contents
of this Volume

Previous Article

Next Article
 


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
dahmen@mathematik.tu-darmstadt.de



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

[ Fulltext-pdf  (319  KB)] for subscribers only.