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Isometric Group Actions on Hilbert Spaces: Structure of Orbits

Published online by Cambridge University Press:  20 November 2018

Yves de Cornulier ,
Romain Tessera  and
Alain Valette
Yves de Cornulier
Affiliation:
IRMAR, Campus de Beaulieu, 35042 Rennes Cedex, France e-mail:yves.decornulier@univ-rennes1.fr
Romain Tessera
Affiliation:
Department of Mathematics, Stevenson Center, Vanderbilt University, Nashville, TN 37240 e-mail:romain.a.tessera@vanderbilt.edu
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Abstract

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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

22D1043A3520F69affine actionsHilbert spacesminimal actionsnilpotent groups
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 60 , Issue 5 , October 2008 , pp. 1001 - 1009
Copyright
Copyright © Canadian Mathematical Society 2008

References

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