Locally compact groups with every isometric action bounded or proper

Romain Tessera; Alain Valette; Corina-Gabriela Ciobotaru

doi:10.1142/S1793525319500547

Locally compact groups with every isometric action bounded or proper

Romain Tessera
, Alain Valette
, Corina-Gabriela Ciobotaru

Research output: Contribution to journal/Conference contribution in journal/Contribution to newspaper › Journal article › Research › peer-review

1 Citation (Scopus)

Abstract

A locally compact group G has property PL if every isometric G-action either has bounded orbits or is (metrically) proper. For p ≥ 1, say that G has property BP p if the same alternative holds for the smaller class of affine isometric actions on Lp-spaces. We explore properties PL and BP p and prove that they are equivalent for some interesting classes of groups: abelian groups, amenable almost connected Lie groups, amenable linear algebraic groups over a local field of characteristic 0. The appendix provides new examples of groups with property PL, including nonlinear ones.

Original language	English
Journal	Journal of Topology and Analysis
Volume	12
Issue	2
Pages (from-to)	267-292
Number of pages	26
ISSN	1793-5253
DOIs	https://doi.org/10.1142/S1793525319500547
Publication status	Published - 1 Jun 2020
Externally published	Yes

Keywords

bounded orbits
Howe-Moore property
L p -spaces
Metrically proper isometric actions

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10.1142/S1793525319500547

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title = "Locally compact groups with every isometric action bounded or proper",

abstract = "A locally compact group G has property PL if every isometric G-action either has bounded orbits or is (metrically) proper. For p ≥ 1, say that G has property BP p if the same alternative holds for the smaller class of affine isometric actions on Lp-spaces. We explore properties PL and BP p and prove that they are equivalent for some interesting classes of groups: abelian groups, amenable almost connected Lie groups, amenable linear algebraic groups over a local field of characteristic 0. The appendix provides new examples of groups with property PL, including nonlinear ones.",

keywords = "bounded orbits, Howe-Moore property, L p -spaces, Metrically proper isometric actions",

author = "Romain Tessera and Alain Valette and Corina-Gabriela Ciobotaru",

note = "Funding Information: The second author would like to thank the Isaac Newton Institute for Mathematical Sciences, Cambridge for support and hospitality during the programme Non-Positive Curvature where work on this paper was finalized. This work was supported by EPSRC Grant No. EP/K032208/1. Publisher Copyright: {\textcopyright} 2020 World Scientific Publishing Company.",

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T1 - Locally compact groups with every isometric action bounded or proper

AU - Tessera, Romain

AU - Valette, Alain

AU - Ciobotaru, Corina-Gabriela

N1 - Funding Information: The second author would like to thank the Isaac Newton Institute for Mathematical Sciences, Cambridge for support and hospitality during the programme Non-Positive Curvature where work on this paper was finalized. This work was supported by EPSRC Grant No. EP/K032208/1. Publisher Copyright: © 2020 World Scientific Publishing Company.

PY - 2020/6/1

Y1 - 2020/6/1

N2 - A locally compact group G has property PL if every isometric G-action either has bounded orbits or is (metrically) proper. For p ≥ 1, say that G has property BP p if the same alternative holds for the smaller class of affine isometric actions on Lp-spaces. We explore properties PL and BP p and prove that they are equivalent for some interesting classes of groups: abelian groups, amenable almost connected Lie groups, amenable linear algebraic groups over a local field of characteristic 0. The appendix provides new examples of groups with property PL, including nonlinear ones.

AB - A locally compact group G has property PL if every isometric G-action either has bounded orbits or is (metrically) proper. For p ≥ 1, say that G has property BP p if the same alternative holds for the smaller class of affine isometric actions on Lp-spaces. We explore properties PL and BP p and prove that they are equivalent for some interesting classes of groups: abelian groups, amenable almost connected Lie groups, amenable linear algebraic groups over a local field of characteristic 0. The appendix provides new examples of groups with property PL, including nonlinear ones.

KW - bounded orbits

KW - Howe-Moore property

KW - L p -spaces

KW - Metrically proper isometric actions

UR - https://www.scopus.com/pages/publications/85054527608

U2 - 10.1142/S1793525319500547

DO - 10.1142/S1793525319500547

M3 - Journal article

AN - SCOPUS:85054527608

SN - 1793-5253

VL - 12

SP - 267

EP - 292

JO - Journal of Topology and Analysis

JF - Journal of Topology and Analysis

IS - 2

ER -

Locally compact groups with every isometric action bounded or proper

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Keywords

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