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Bounded rank of C*-algebras

Alex Chigogidze·Vesko Valov
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Abstract

We introduce a concept of the bounded rank (with respect to a positive constant) for unital C*-algebras as a modification of the usual real rank and present a series of conditions insuring that bounded and real ranks coincide. These observations are then used to prove that for a given $n$ and $K > 0$ there exists a separable unital C*-algebra $Z_{n}^{K}$ such that every other separable unital C*-algebra of bounded rank with respect to $K$ at most $n$ is a quotient of $Z_{n}^{K}$.

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Alex Chigogidze, Vesko Valov. 2002-04-07. Bounded rank of C*-algebras. https://arxiv.org/abs/math/0109100

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