Geodesic
Isometric Group Actions on Hilbert Spaces: Structure of Orbits
Canadian journal of mathematics, Tome 60 (2008) no. 5, pp. 1001-1009

Voir la notice de l'article provenant de la source Cambridge University Press

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.
DOI : 10.4153/CJM-2008-044-4
Mots-clés : 22D10, 43A35, 20F69, affine actions, Hilbert spaces, minimal actions, nilpotent groups 
Cornulier, Yves de; Tessera, Romain. Isometric Group Actions on Hilbert Spaces: Structure of Orbits. Canadian journal of mathematics, Tome 60 (2008) no. 5, pp. 1001-1009. doi: 10.4153/CJM-2008-044-4
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