Regularity in Milnor's Sense for Ascending Unions of Banach-Lie Groups
Journal of Lie Theory, Tome 24 (2014) no. 2, pp. 545-560
Voir la notice de l'article provenant de la source Heldermann Verlag
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.
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.
Classification :
58B25, 22E65
Mots-clés : 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
Mots-clés : 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
Affiliations des auteurs :
Rafael Dahmen 1
Rafael Dahmen. Regularity in Milnor's Sense for Ascending Unions of Banach-Lie Groups. Journal of Lie Theory, Tome 24 (2014) no. 2, pp. 545-560. http://geodesic.mathdoc.fr/item/JOLT_2014_24_2_a11/
@article{JOLT_2014_24_2_a11,
author = {Rafael Dahmen},
title = {Regularity in {Milnor's} {Sense} for {Ascending} {Unions} of {Banach-Lie} {Groups}},
journal = {Journal of Lie Theory},
pages = {545--560},
year = {2014},
volume = {24},
number = {2},
url = {http://geodesic.mathdoc.fr/item/JOLT_2014_24_2_a11/}
}