Isometric group actions on Hilbert spaces: Structure of orbits

Yves De Cornulier; Romain Tessera; Alain Valette

doi:10.4153/cjm-2008-044-4

Isometric group actions on Hilbert spaces: Structure of orbits

Yves De Cornulier
, Romain Tessera
, Alain Valette

UMR 6625
Vanderbilt University
University of Neuchatel

Résultats de recherche: Contribution à un journal › Article › Revue par des pairs

5 Citations (Scopus)

Résumé

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.

langue originale	Anglais
Pages (de - à)	1001-1009
Nombre de pages	9
journal	Canadian Journal of Mathematics
Volume	60
Numéro de publication	5
Les DOIs	https://doi.org/10.4153/cjm-2008-044-4
état	Publié - 1 janv. 2008
Modification externe	Oui

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10.4153/cjm-2008-044-4

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title = "Isometric group actions on Hilbert spaces: Structure of orbits",

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",

author = "\{De Cornulier\}, Yves and Romain Tessera and Alain Valette",

year = "2008",

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T1 - Isometric group actions on Hilbert spaces

T2 - Structure of orbits

AU - De Cornulier, Yves

AU - Tessera, Romain

AU - Valette, Alain

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N2 - 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.

AB - 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.

KW - Affine actions

KW - Hilbert spaces

KW - Minimal actions

KW - Nilpotent groups

U2 - 10.4153/cjm-2008-044-4

DO - 10.4153/cjm-2008-044-4

M3 - Article

AN - SCOPUS:53549126367

SN - 0008-414X

VL - 60

SP - 1001

EP - 1009

JO - Canadian Journal of Mathematics

JF - Canadian Journal of Mathematics

IS - 5

ER -

Isometric group actions on Hilbert spaces: Structure of orbits

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