Obstructions to a general characterization of graph correspondences

Abstract

For a countable discrete space V, every nondegenerate separable C*-correspondence over c_0(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.

major revision; stated some results in greater generality

References in corpus (1)

• Hilbert $C^{\ast }$-bimodules over commutative $C^{\ast }$-algebras and an isomorphism condition for quantum Heisenberg manifolds

Cited by in corpus (1)

• Reconstruction of topological graphs and their Hilbert bimodules