Hereditary C*-subalgebras of graph C*-algebras

@article{Arklint2020HereditaryCO,
  title={Hereditary C*-subalgebras of graph C*-algebras},
  author={Sara E. Arklint and James Gabe and Efren Ruiz},
  journal={arXiv: Operator Algebras},
  year={2020},
  pages={99}
}
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… 
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