Hereditary C^*-subalgebras of graph C^*-algebras

2016/04/11 by Sara E. Arklint, Arklint, Sara E., James Gabe +3
Mathematics · #46L55 #FOS: Mathematics #Operator Algebras (math.OA) #math.OA #msc:46L55

paper · pdf · doi:10.48550/arxiv.1604.03085

23 pages. Ver 2: 24 pages, minor changes to introduction, bibliography updated

arxiv created 2017/01/31 · arxiv updated 2017/02/01

Abstract

We show that a C^*-algebra \mathfrakA which is stably isomorphic to a unital graph C^*-algebra, is isomorphic to a graph C^*-algebra if and only if it admits an approximate unit of projections. As a consequence, a hereditary C^*-subalgebra of a unital real rank zero graph C^*-algebra is isomorphic to a graph C^*-algebra. Furthermore, if a C^*-algebra \mathfrakA admits an approximate unit of projections, then its minimal unitization is isomorphic to a graph C^*-algebra if and only if \mathfrakA is stably isomorphic to a unital graph C^*-algebra.

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