Obstructions to a general characterization of graph correspondences

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Abstract

For a countable discrete space V, every nondegenerate separable C*-correspondence over c0(V) is isomorphic to one coming from a directed graph with vertex set V. In this paper we demonstrate why the analogous characterizations fail to hold for higher-rank graphs (where one considers product systems of C*-correspondences) and for topological graphs (where V is locally compact Hausdorff), and we discuss the obstructions that arise.

Original languageEnglish (US)
Pages (from-to)169-188
Number of pages20
JournalJournal of the Australian Mathematical Society
Volume95
Issue number2
DOIs
StatePublished - Oct 1 2013

Keywords

  • C*-correspondences
  • Hilbert modules
  • K-graphs
  • Topological graphs

ASJC Scopus subject areas

  • Mathematics(all)

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