On purely infinite 𝐶*-algebras

Jeong, Ja A; Lee, Sa Ge

doi:10.1090/S0002-9939-1993-1113642-1

On purely infinite $C\sp *$ -algebras

Authors: Ja A Jeong and Sa Ge Lee
Journal: Proc. Amer. Math. Soc. 117 (1993), 679-682
MSC: Primary 46L05
DOI: https://doi.org/10.1090/S0002-9939-1993-1113642-1
MathSciNet review: 1113642
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Abstract: We find conditions under which a quotient ${C^{\ast}}$ -algebra of a purely infinite ${C^{\ast}}$ -algebra becomes purely infinite. S. Zhang proved that if is a $\sigma$ -unital, simple, purely infinite ${C^{\ast}}$ -algebra, then a hereditary ${C^{\ast}}$ -subalgebra ${A_x}$ is a stable or unital for each of ${A_ + }$ . We prove the converse for a completely $\sigma$ -unital infinite simple ${C^{\ast}}$ -algebra.

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