Hereditary $C^*$subalgebras of graph $C^*$algebras
Abstract
We show that a $C^*$algebra $\mathfrak{A}$ 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 $\mathfrak{A}$ admits an approximate unit of projections, then its minimal unitization is isomorphic to a graph $C^*$algebra if and only if $\mathfrak{A}$ is stably isomorphic to a unital graph $C^*$algebra.
 Publication:

arXiv eprints
 Pub Date:
 April 2016
 arXiv:
 arXiv:1604.03085
 Bibcode:
 2016arXiv160403085A
 Keywords:

 Mathematics  Operator Algebras;
 46L55
 EPrint:
 23 pages. Ver 2: 24 pages, minor changes to introduction, bibliography updated