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Proceedings of the American Mathematical Society

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

 

 

A property of purely infinite simple $ C\sp *$-algebras


Author: Shuang Zhang
Journal: Proc. Amer. Math. Soc. 109 (1990), 717-720
MSC: Primary 46L05
MathSciNet review: 1010004
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Abstract: An alternative proof is given for the fact ([13]) that a purely infinite, simple $ {C^*}$-algebra has the FS property: the set of self-adjoint elements with finite spectrum is norm dense in the set of all self-adjoint elements. In particular, the Cuntz algebras $ {O_n}(2 \leq n \leq + \infty )$ and the Cuntz-Krieger algebras $ {O_A}$, if $ A$ is an irreducible matrix, have the FS property. This answers a question raised in [2, 2.10] concerning the structure of projections in the Cuntz algebras. Moreover, many corona algebras and multiplier algebras have the FS property.


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DOI: https://doi.org/10.1090/S0002-9939-1990-1010004-X
Keywords: Purely infinite simple $ {C^*}$-algebras, projections, the Cuntz algebras
Article copyright: © Copyright 1990 American Mathematical Society