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Isometric Group Actions on Hilbert Spaces: Structure of Orbits

  Published:2008-10-01
 Printed: Oct 2008
  • Yves de Cornulier
  • Romain Tessera
  • Alain Valette
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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: affine actions, Hilbert spaces, minimal actions, nilpotent groups affine actions, Hilbert spaces, minimal actions, nilpotent groups
MSC Classifications: 22D10, 43A35, 20F69 show english descriptions Unitary representations of locally compact groups
Positive definite functions on groups, semigroups, etc.
Asymptotic properties of groups
22D10 - Unitary representations of locally compact groups
43A35 - Positive definite functions on groups, semigroups, etc.
20F69 - Asymptotic properties of groups
 

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