A property of purely infinite simple -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 -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 and the Cuntz-Krieger algebras , if 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 -algebras,
projections,
the Cuntz algebras

Article copyright:
© Copyright 1990
American Mathematical Society