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

Laustsen, Niels Jakob; White, Jared

doi:10.1090/proc/13931

An infinite C-algebra with a dense, stably finite -subalgebra
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by Niels Jakob Laustsen and Jared T. White PDF

Proc. Amer. Math. Soc. 146 (2018), 2523-2528 Request permission

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.

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