### 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

### Cite this

*C**-algebras and integrable actions.

*Mathematische Zeitschrift*,

*250*(2), 393-410. https://doi.org/10.1007/s00209-004-0759-4

**Bounded trace C*-algebras and integrable actions.** / Archbold, Robert J; Deicke, C.

Research output: Contribution to journal › Article

*C**-algebras and integrable actions',

*Mathematische Zeitschrift*, vol. 250, no. 2, pp. 393-410. https://doi.org/10.1007/s00209-004-0759-4

*C**-algebras and integrable actions. Mathematische Zeitschrift. 2005;250(2):393-410. https://doi.org/10.1007/s00209-004-0759-4

}

TY - JOUR

T1 - Bounded trace C*-algebras and integrable actions

AU - Archbold, Robert J

AU - Deicke, C.

PY - 2005

Y1 - 2005

N2 - 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.

AB - 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.

KW - TRANSFORMATION GROUPS

KW - STAR-ALGEBRAS

KW - REPRESENTATIONS

KW - MULTIPLICITY

KW - IDEALS

U2 - 10.1007/s00209-004-0759-4

DO - 10.1007/s00209-004-0759-4

M3 - Article

VL - 250

SP - 393

EP - 410

JO - Mathematische Zeitschrift

JF - Mathematische Zeitschrift

SN - 0025-5874

IS - 2

ER -