Strength of convergence in the orbit space of a transformation group

Robert J Archbold, A. an Huef

Research output: Contribution to journalArticle

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 languageEnglish
Pages (from-to)90-121
Number of pages31
JournalJournal of Functional Analysis
Volume235
DOIs
Publication statusPublished - 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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