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 
induced by α is free and the G-orbits are locally closed. We show that the crossed product A×
α
G has bounded trace if and only if G acts integrably (in the sense of Rieffel and an Huef) on . 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.
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Mathemactics Subject Classification (1991): 46L55
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Archbold, R., Deicke, K. Bounded trace C*-algebras and integrable actions. Math. Z. 250, 393–410 (2005). https://doi.org/10.1007/s00209-004-0759-4
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DOI: https://doi.org/10.1007/s00209-004-0759-4