Strength of convergence in the orbit space of a groupoid

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:383

Article

Hazlewood, Robert²  Huef, Astrid An¹ 

[1] Univ Otago, Dept Math & Stat, Dunedin 9054, New Zealand

[2] Univ New S Wales, Sch Math & Stat, Sydney, NSW 2052, Australia

关键词: 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;   

DOI  :  10.1016/j.jmaa.2011.04.061

来源: Elsevier

【 摘 要 】

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 G((0)) of G. We show that the notions of strength of convergence of {x(n)} 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. (C) 2011 Elsevier Inc. All rights reserved.

【 授权许可】

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