1. CJM 2008 (vol 60 pp. 1001)
|Isometric Group Actions on Hilbert Spaces: Structure of Orbits |
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.
Keywords:affine actions, Hilbert spaces, minimal actions, nilpotent groups
Categories:22D10, 43A35, 20F69