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Isometric Group Actions on Hilbert Spaces: Structure of Orbits

  • Yves de Cornulier (a1), Romain Tessera (a2) and Alain Valette
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.

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References
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[CTV] Cornulier, Y. de, Tessera, R., and Valette, A., Isometric group actions on Hilbert spaces: growth of cocycles . Geom. funct. Anal. 17(2007), no. 3, 770792.
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Canadian Journal of Mathematics
  • ISSN: 0008-414X
  • EISSN: 1496-4279
  • URL: /core/journals/canadian-journal-of-mathematics
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