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Strength of convergence in the orbit space of a groupoid |
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| Authors: | Robert Hazlewood |
| Affiliation: | a School of Mathematics and Statistics, The University of New South Wales, Sydney, NSW 2052, Australia b Department of Mathematics and Statistics, University of Otago, PO Box 56, Dunedin 9054, New Zealand |
| Abstract: | Let G be a second-countable locally-compact Hausdorff groupoid with a Haar system, and let {xn} be a sequence in the unit space G(0) of G. We show that the notions of strength of convergence of {xn} in the orbit space G(0)/G 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. |
| Keywords: | Groupoid C?-algebra of a groupoid Spectrum of a C?-algebra Multiplicity of a representation k-times convergence Orbit space Groupoid of a directed graph |
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