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 |
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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