Hereditary C*-subalgebras of graph C*-algebras
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We show that a C*-algebra 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 A admits an approximate unit of projections, then its minimal unitization is isomorphic to a graph C*-algebra if and only if A is stably isomorphic to a unital graph C*-algebra.
Originalsprog | Engelsk |
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Tidsskrift | Journal of Operator Theory |
Vol/bind | 84 |
Udgave nummer | 1 |
Sider (fra-til) | 99-126 |
ISSN | 0379-4024 |
DOI | |
Status | Udgivet - 2020 |
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