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OBSTRUCTIONS TO A GENERAL CHARACTERIZATION OF GRAPH CORRESPONDENCES

Part of: Selfadjoint operator algebras

Published online by Cambridge University Press:  07 June 2013

S. KALISZEWSKI ,
NURA PATANI  and
JOHN QUIGG
S. KALISZEWSKI*
Affiliation:
School of Mathematical and Statistical Sciences, Arizona State University, Tempe, Arizona 85287, USA email [email protected]@asu.edu
NURA PATANI
Affiliation:
School of Mathematical and Statistical Sciences, Arizona State University, Tempe, Arizona 85287, USA email [email protected]@asu.edu
JOHN QUIGG
Affiliation:
School of Mathematical and Statistical Sciences, Arizona State University, Tempe, Arizona 85287, USA email [email protected]@asu.edu
*
✉[email protected]
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Abstract

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For a countable discrete space $V$, every nondegenerate separable ${C}^{\ast } $-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}^{\ast } $-correspondences) and for topological graphs (where $V$ is locally compact Hausdorff), and we discuss the obstructions that arise.

Keywords

Hilbert modulesC∗-correspondencesk-graphstopological graphs

MSC classification

Secondary: 46L08: $C^*$-modules
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 95 , Issue 2 , October 2013 , pp. 169 - 188
Copyright
Copyright ©2013 Australian Mathematical Publishing Association Inc. 

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