Comparison Properties of the Cuntz Semigroup and Applications to C* -algebras. (1st February 2018)

• Record Type: Journal Article
• Authors: Bosa, Joan; Petzka, Henning
• Is Part Of: Canadian journal of mathematics. Volume 70:Number 1(2018)
• Page Start: 26
• Page End: 52
• Publication Date: 2018-02-01
• Subjects: 46L35 -- 06F05 -- 46L05 -- 19K14; classification of C*-algebras -- cuntz semigroup; Mathematics -- Periodicals; Mathematics; Electronic journals; Periodicals; 510
• DOI: 10.4153/CJM-2016-049-8
• Languages: English
• ISSNs: 0008-414X

Abstract

Abstract: 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 $\text{CFP}$ .