Isometric group actions on Hilbert spaces: structure of orbits

Details Isometric group actions on Hilbert spaces: structure of orbits Isometric group actions on Hilbert spaces: structure of orbits

2006-04-03

arxiv.org/abs/math/0604051v1

Canadian Math. J. 60 (2008), no. 5, 1001-1009

Mathematics

Group Theory

12 pages, to appear in Canadian Math. J

Scientific paper

10.4153/CJM-2008-044-4

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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