English

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.

Keywords

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

R2 v1 2026-07-22T17:33:46.877Z