An infinite C*-algebra with a dense, stably finite *-subalgebra

Laustsen, Niels Jakob and White, Jared (2018) An infinite C*-algebra with a dense, stably finite *-subalgebra. Proceedings of the American Mathematical Society, 146. pp. 2523-2528. ISSN 0002-9939

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Abstract

We construct a unital pre-C*-algebra $ A_0$ which is stably finite, in the sense that every left invertible square matrix over $ A_0$ is right invertible, while the C*-completion of $ A_0$ contains a nonunitary isometry, and so it is infinite.