Isometric group actions on Hilbert spaces: structure of orbits
Group Theory
2010-08-04 v1 Functional Analysis
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.
Cite
@article{arxiv.math/0604051,
title = {Isometric group actions on Hilbert spaces: structure of orbits},
author = {Yves de Cornulier and Romain Tessera and Alain Valette},
journal= {arXiv preprint arXiv:math/0604051},
year = {2010}
}
Comments
12 pages, to appear in Canadian Math. J