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Isometric group actions on Hilbert spaces: structure of orbits

Research paper by Yves de Cornulier, Romain Tessera, Alain Valette

Indexed on: 03 Apr '06Published on: 03 Apr '06Published in: Mathematics - Group Theory



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.