L^1-regularity of strong ILB-Lie groups
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866916422785957888 |
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| author | Glockner, Helge Suri, Ali |
| author_facet | Glockner, Helge Suri, Ali |
| contents | If G is a Lie group modeled on a Fréchet 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 Fréchet-Lie groups considered by Hermas and Bedida. Examples are given. Notably, we obtain L^1-regularity for certain weighted diffeomorphism groups. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_02909 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | L^1-regularity of strong ILB-Lie groups Glockner, Helge Suri, Ali Functional Analysis 22E65 (primary), 34A12, 46E30, 46E40 (secondary) If G is a Lie group modeled on a Fréchet 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 Fréchet-Lie groups considered by Hermas and Bedida. Examples are given. Notably, we obtain L^1-regularity for certain weighted diffeomorphism groups. |
| title | L^1-regularity of strong ILB-Lie groups |
| topic | Functional Analysis 22E65 (primary), 34A12, 46E30, 46E40 (secondary) |
| url | https://arxiv.org/abs/2410.02909 |