Abstract
For a compact group G acting continuously on a Banach Lie group U, we prove that maps G → 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 G-action, compact Lie G and U) and de la Harpe-Karoubi (trivial G-action, U:=invertible elements of a Banach algebra). The obvious analogues for higher cocycles also hold for abelian U.
| Original language | English |
|---|---|
| Pages (from-to) | 447-453 |
| Number of pages | 7 |
| Journal | Journal of Lie Theory |
| Volume | 35 |
| Issue number | 3 |
| State | Published - 2025 |
Keywords
- Baker-Campbell-Hausdorff
- Banach Lie group
- Haar measure
- Hyers-Ulam-Rassias stability
- almost-morphism
- averaging
- coboundary
- cocycle
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