Strength of convergence in the orbit space of a groupoid

2010/06/16 by Hazlewood, Robert, Huef, Astrid an
#46L #FOS: Mathematics #Operator Algebras (math.OA)

paper · doi:10.48550/arxiv.1006.3115

Abstract

Let G be a second-countable locally-compact Hausdorff groupoid with a Haar system, and let x_n be a sequence in the unit space of G. We show that the notions of strength of convergence of x_n in the orbit space and measure-theoretic accumulation along the orbits are equivalent ways of realising multiplicity numbers associated to a sequence of induced representation of the groupoid C*-algebra.

Related

• Groupoid C*-algebras with Hausdorff Spectrum
• Strength of convergence in the orbit space of a transformation group
• The orbit space of groupoids whose C^*-algebras are GCR
• The orbit spaces of groupoids whose C^*-algebras are CCR
• Haar Systems on Equivalent Groupoids