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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

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 $ A/I$ of a purely infinite $ {C^{\ast}}$-algebra $ A$ becomes purely infinite. S. Zhang proved that if $ A$ 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 $ x$ of $ {A_ + }$. We prove the converse for a completely $ \sigma $-unital infinite simple $ {C^{\ast}}$-algebra.


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DOI: https://doi.org/10.1090/S0002-9939-1993-1113642-1
Keywords: Purely infinite $ {C^{\ast}}$-algebras, annihilators, hereditary $ {C^{\ast}}$-subalgebras
Article copyright: © Copyright 1993 American Mathematical Society