Isometric group actions on Hilbert spaces: structure of orbits
Yves de Cornulier, Romain Tessera, Alain Valette
math.GRarXiv:math/0604051
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.
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