Comparison Properties of the Cuntz Semigroup and Applications to C*-algebras

摘要

We study comparison properties in the category Cu aiming to lift results to the C*-algebraic setting. We introduce a new comparison property and relate it to both the corona factorization property (CFP) and omega-comparison. We show differences of all properties by providing examples that suggest that the corona factorization for C*-algebras might allow for both finite and infinite projections. In addition, we show that Rordam's simple, nuclear C*-algebra with a finite and an infinite projection does not have the CFP.