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arXiv · 2410.02909

L^1-regularity of strong ILB-Lie groups

Helge Glockner·Ali Suri
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Abstract

If G is a Lie group modeled on a Fr\'echet space, let e be its neutral element and g be its Lie algebra. We show that every strong ILB-Lie group G is L^1-regular in the sense that each f in L^1([0,1],g) is the right logarithmic derivative of some absolutely continuous curve c in G with c(0)=e and the map from L^1([0,1],g) to C([0,1],G) taking f to c is smooth. More generally, the conclusion holds for a class of Fr\'echet-Lie groups considered by Hermas and Bedida. Examples are given. Notably, we obtain L^1-regularity for certain weighted diffeomorphism groups.

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Helge Glockner, Ali Suri. 2024-10-03. L^1-regularity of strong ILB-Lie groups. https://arxiv.org/abs/2410.02909

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