Remote Access Proceedings of the American Mathematical Society
Green Open Access

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
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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.

References [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 46L05

Retrieve articles in all journals with MSC: 46L05

Additional Information

Keywords: Purely infinite simple $ {C^*}$-algebras, projections, the Cuntz algebras
Article copyright: © Copyright 1990 American Mathematical Society

American Mathematical Society