Hereditary C*-subalgebras of graph C*-algebras
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Hereditary C*-subalgebras of graph C*-algebras. / Arklint, Sara E.; Gabe, James; Ruiz, Efren.
In: Journal of Operator Theory, Vol. 84, No. 1, 2020, p. 99-126.Research output: Contribution to journal › Journal article › Research › peer-review
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TY - JOUR
T1 - Hereditary C*-subalgebras of graph C*-algebras
AU - Arklint, Sara E.
AU - Gabe, James
AU - Ruiz, Efren
PY - 2020
Y1 - 2020
N2 - 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.
AB - 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.
KW - Graph C-algebras
KW - Hereditary C-subalgebras
UR - http://www.scopus.com/inward/record.url?scp=85088273747&partnerID=8YFLogxK
U2 - 10.7900/jot.2019jan21.2230
DO - 10.7900/jot.2019jan21.2230
M3 - Journal article
AN - SCOPUS:85088273747
VL - 84
SP - 99
EP - 126
JO - Journal of Operator Theory
JF - Journal of Operator Theory
SN - 0379-4024
IS - 1
ER -
ID: 249247356