## 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 language | English |
---|---|

Pages (from-to) | 393-410 |

Number of pages | 17 |

Journal | Mathematische Zeitschrift |

Volume | 250 |

Issue number | 2 |

DOIs | |

Publication status | Published - 2005 |

## Keywords

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

## Fingerprint

Dive into the research topics of 'Bounded trace*C**-algebras and integrable actions'. Together they form a unique fingerprint.