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On the Radius of Comparison of a Commutative C*-algebra

  • George A. Elliott (a1) and Zhuang Niu (a2)

Abstract.

Let $X$ be a compact metric space. A lower bound for the radius of comparison of the ${{\text{C}}^{*}}$ -algebra $\text{C}\left( X \right)$ is given in terms of ${{\dim}_{\mathbb{Q}}}\,X$ , where ${{\dim}_{\mathbb{Q}}}\,X$ is the cohomological dimension with rational coefficients. If ${{\dim}_{\mathbb{Q}}}\,X\,=\,\dim\,X\,=\,d$ , then the radius of comparison of the ${{\text{C}}^{*}}$ -algebra $C\left( X \right)$ is $\max \left\{ 0,\,\left( d\,-\,1 \right)/\,2\,-\,1 \right\}$ if $d$ is odd, and must be either ${d}/{2}\;\,-\,1$ or ${d}/{2}\;\,-\,2$ if $d$ is even (the possibility ${d}/{2}\;\,-\,1$ does occur, but we do not know if the possibility ${d}/{2}\;\,-\,2$ can also occur).

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References

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On the Radius of Comparison of a Commutative C*-algebra

  • George A. Elliott (a1) and Zhuang Niu (a2)

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