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Comparison Properties of the Cuntz Semigroup and Applications to C* -algebras
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- Journal:
- Canadian Journal of Mathematics / Volume 70 / Issue 1 / 01 February 2018
- Published online by Cambridge University Press:
- 20 November 2018, pp. 26-52
- Print publication:
- 01 February 2018
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- Article
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We study comparison properties in the category
$\text{Cu}$ aiming to lift results to the 
${{\text{C}}^{\text{*}}}$-algebraic setting. We introduce a new comparison property and relate it to both the corona factorization property 
$\left( \text{CFP} \right)$ and 
$\omega $-comparison. We show differences of all properties by providing examples that suggest that the corona factorization for ${{\text{C}}^{\text{*}}}$-algebras might allow for both finite and infinite projections. In addition, we show that Rørdam's simple, nuclear ${{\text{C}}^{\text{*}}}$-algebra with a finite and an inifnite projection does not have the 
$\text{CFP}$.
