Journal of Lie Theory

no. 2
Regularity in Milnor's Sense for Ascending Unions of Banach-Lie Groups
Journal of Lie Theory, Volume 24 (2014) no. 2, pp. 545-560
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.
DOI: 10.5802/jolt.796
Classification: 58B25, 22E65
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 
@article{JOLT_2014_24_2_a11,
     author = {R. 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},
     doi = {10.5802/jolt.796},
     zbl = {1310.22016},
     url = {https://jolt.centre-mersenne.org/articles/10.5802/jolt.796/}
}
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R. Dahmen. Regularity in Milnor's Sense for Ascending Unions of Banach-Lie Groups. Journal of Lie Theory, Volume 24 (2014) no. 2, pp. 545-560. doi: 10.5802/jolt.796

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