Strength of convergence in the orbit space of a transformation group

Robert J Archbold; A. an Huef

doi:10.1016/j.jfa.2005.10.001

Strength of convergence in the orbit space of a transformation group

Robert J Archbold, A. an Huef

Mathematical Science

Research output: Contribution to journal › Article › peer-review

5 Citations (Scopus)

Abstract

Let (G, X) be a second-countable transformation group with G acting freely on X. It is shown that measure-theoretic accumulation of the action and topological strength of convergence in the orbit space X/G provide equivalent ways of quantifying the extent of nonproperness of the action. These notions are linked via the representation theory of the transformation-group C-*-algebra C-0(X) x G. (C) 2005 Elsevier Inc. All rights reserved.

Original language	English
Pages (from-to)	90-121
Number of pages	31
Journal	Journal of Functional Analysis
Volume	235
DOIs	https://doi.org/10.1016/j.jfa.2005.10.001
Publication status	Published - Jun 2006

Keywords

transformation group
orbit space
k-times convergence
spectrum of a C*-algebra
multiplicity of a representation
trace function
C-ASTERISK-ALGEBRAS
STAR-ALGEBRAS
BOUNDED TRACE
IRREDUCIBLE REPRESENTATIONS
INTEGRABLE ACTIONS
LOWER MULTIPLICITY
LIE-GROUPS

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10.1016/j.jfa.2005.10.001

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title = "Strength of convergence in the orbit space of a transformation group",

abstract = "Let (G, X) be a second-countable transformation group with G acting freely on X. It is shown that measure-theoretic accumulation of the action and topological strength of convergence in the orbit space X/G provide equivalent ways of quantifying the extent of nonproperness of the action. These notions are linked via the representation theory of the transformation-group C-*-algebra C-0(X) x G. (C) 2005 Elsevier Inc. All rights reserved.",

keywords = "transformation group, orbit space, k-times convergence, spectrum of a C*-algebra, multiplicity of a representation, trace function, C-ASTERISK-ALGEBRAS, STAR-ALGEBRAS, BOUNDED TRACE, IRREDUCIBLE REPRESENTATIONS, INTEGRABLE ACTIONS, LOWER MULTIPLICITY, LIE-GROUPS",

author = "Archbold, {Robert J} and {an Huef}, A.",

year = "2006",

month = jun,

doi = "10.1016/j.jfa.2005.10.001",

language = "English",

volume = "235",

pages = "90--121",

journal = "Journal of Functional Analysis",

issn = "0022-1236",

publisher = "Academic Press Inc.",

}

TY - JOUR

T1 - Strength of convergence in the orbit space of a transformation group

AU - Archbold, Robert J

AU - an Huef, A.

PY - 2006/6

Y1 - 2006/6

N2 - Let (G, X) be a second-countable transformation group with G acting freely on X. It is shown that measure-theoretic accumulation of the action and topological strength of convergence in the orbit space X/G provide equivalent ways of quantifying the extent of nonproperness of the action. These notions are linked via the representation theory of the transformation-group C-*-algebra C-0(X) x G. (C) 2005 Elsevier Inc. All rights reserved.

AB - Let (G, X) be a second-countable transformation group with G acting freely on X. It is shown that measure-theoretic accumulation of the action and topological strength of convergence in the orbit space X/G provide equivalent ways of quantifying the extent of nonproperness of the action. These notions are linked via the representation theory of the transformation-group C-*-algebra C-0(X) x G. (C) 2005 Elsevier Inc. All rights reserved.

KW - transformation group

KW - orbit space

KW - k-times convergence

KW - spectrum of a C-algebra

KW - multiplicity of a representation

KW - trace function

KW - C-ASTERISK-ALGEBRAS

KW - STAR-ALGEBRAS

KW - BOUNDED TRACE

KW - IRREDUCIBLE REPRESENTATIONS

KW - INTEGRABLE ACTIONS

KW - LOWER MULTIPLICITY

KW - LIE-GROUPS

U2 - 10.1016/j.jfa.2005.10.001

DO - 10.1016/j.jfa.2005.10.001

M3 - Article

SN - 0022-1236

VL - 235

SP - 90

EP - 121

JO - Journal of Functional Analysis

JF - Journal of Functional Analysis

ER -

Strength of convergence in the orbit space of a transformation group

Abstract

Keywords

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