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arXiv:math/0604051 [math.GR]AbstractReferencesReviewsResources

Isometric group actions on Hilbert spaces: structure of orbits

Yves de Cornulier, Romain Tessera, Alain Valette

Published 2006-04-03Version 1

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.

Comments: 12 pages, to appear in Canadian Math. J
Journal: Canadian Math. J. 60 (2008), no. 5, 1001-1009
Categories: math.GR, math.FA
Subjects: 22D10, 43A35, 20F69
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