A property of purely infinite simple 𝐶*-algebras

Zhang, Shuang

doi:10.1090/S0002-9939-1990-1010004-X

A property of purely infinite simple $C^ *$-algebras
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Proc. Amer. Math. Soc. 109 (1990), 717-720 Request permission

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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