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Isometric group actions on Hilbert spaces: structure of orbits

Yves de Cornulier·Romain Tessera·Alain Valette
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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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Yves de Cornulier, Romain Tessera, Alain Valette. 2006-04-03. Isometric group actions on Hilbert spaces: structure of orbits. https://doi.org/10.4153/cjm-2008-044-4

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