Straightening Banach-Lie-Group-Valued Almost-Cocycles
Journal of Lie Theory, Tome 35 (2025) no. 3, pp. 447-453
Voir la notice de l'article provenant de la source Heldermann Verlag
For a compact group $\mathbb{G}$ acting continuously on a Banach Lie group $\mathbb{U}$, we prove that maps $\mathbb{G}\to \mathbb{U}$ close to being 1-cocycles for the action can be deformed analytically into actual 1-cocycles. This recovers Hyers-Ulam stability results of Grove-Karcher-Ruh (trivial $\mathbb{G}$-action, compact Lie $\mathbb{G}$ and $\mathbb{U}$) and de la Harpe-Karoubi (trivial $\mathbb{G}$-action, $\mathbb{U}:=$invertible elements of a Banach algebra). The obvious analogues for higher cocycles also hold for abelian $\mathbb{U}$.
Classification :
22E65, 22C05, 58B25, 46E50, 20J06, 58C15, 22E66, 22D12, 39B82, 46G20, 22E41
Mots-clés : Banach Lie group, cocycle, coboundary, Haar measure, averaging, almost-morphism, Baker-Campbell-Hausdorff, Hyers-Ulam-Rassias stability
Mots-clés : Banach Lie group, cocycle, coboundary, Haar measure, averaging, almost-morphism, Baker-Campbell-Hausdorff, Hyers-Ulam-Rassias stability
Affiliations des auteurs :
Alexandru Chirvasitu 1
Alexandru Chirvasitu. Straightening Banach-Lie-Group-Valued Almost-Cocycles. Journal of Lie Theory, Tome 35 (2025) no. 3, pp. 447-453. http://geodesic.mathdoc.fr/item/JOLT_2025_35_3_a0/
@article{JOLT_2025_35_3_a0,
author = {Alexandru Chirvasitu},
title = {Straightening {Banach-Lie-Group-Valued} {Almost-Cocycles}},
journal = {Journal of Lie Theory},
pages = {447--453},
year = {2025},
volume = {35},
number = {3},
url = {http://geodesic.mathdoc.fr/item/JOLT_2025_35_3_a0/}
}