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On the Radius of Comparison of a Commutative C*-algebra
Published online by Cambridge University Press: 20 November 2018
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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- Copyright © Canadian Mathematical Society 2013
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