Bounded trace C*-algebras and integrable actions

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Abstract

Let G be a second countable group, A be a separable C*-algebra with bounded trace and α a strongly continuous action of G on A. Suppose that the action of G on (A) over cap induced by α is free and the G-orbits are locally closed. We show that the crossed product A x(α) G has bounded trace if and only if G acts integrably ( in the sense of Rieffel and an Huef) on (A) over cap. In the course of this, we show that the extent of non-properness of an integrable action gives rise to a lower bound for the size of the ( finite) upper multiplicities of the irreducible representations of the crossed product.

Original languageEnglish
Pages (from-to)393-410
Number of pages17
JournalMathematische Zeitschrift
Volume250
Issue number2
DOIs
Publication statusPublished - 2005

Keywords

  • TRANSFORMATION GROUPS
  • STAR-ALGEBRAS
  • REPRESENTATIONS
  • MULTIPLICITY
  • IDEALS

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