Geodesic
Comparison Properties of the CuntzSemigroup and Applications to C* -algebras
Canadian journal of mathematics, Tome 70 (2018) no. 1, pp. 26-52

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DOI

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 $\text{CFP}$ .
DOI : 10.4153/CJM-2016-049-8
Mots-clés : 46L35, 06F05, 46L05, 19K14, classification of C*-algebras, cuntz semigroup 
Bosa, Joan; Petzka, Henning. Comparison Properties of the CuntzSemigroup and Applications to C* -algebras. Canadian journal of mathematics, Tome 70 (2018) no. 1, pp. 26-52. doi: 10.4153/CJM-2016-049-8
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     author = {Bosa, Joan and Petzka, Henning},
     title = {Comparison {Properties} of the {CuntzSemigroup} and {Applications} to {C*} -algebras},
     journal = {Canadian journal of mathematics},
     pages = {26--52},
     year = {2018},
     volume = {70},
     number = {1},
     doi = {10.4153/CJM-2016-049-8},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-2016-049-8/}
}
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