Abstract
Our main result is that a finitely generated nilpotent group has no isometric action on an infinite-dimensional Hilbert space with dense orbits. In contrast, we construct such an action with a finitely generated metabelian group.
| Original language | English |
|---|---|
| Pages (from-to) | 1001-1009 |
| Number of pages | 9 |
| Journal | Canadian Journal of Mathematics |
| Volume | 60 |
| Issue number | 5 |
| DOIs | |
| Publication status | Published - 1 Jan 2008 |
| Externally published | Yes |
Keywords
- Affine actions
- Hilbert spaces
- Minimal actions
- Nilpotent groups