2021/03/24 by Thiel, Hannes, Vilalta, Eduard
#46L85 #55M10 #FOS: Mathematics #Operator Algebras (math.OA) #Primary 46L05 #Secondary 54F45
paper · doi:10.48550/arxiv.2103.13062
We show that the dimension of the Cuntz semigroup of a C*-algebra is determined by the dimensions of the Cuntz semigroups of its separable sub-C*-algebras. This allows us to remove separability assumptions from previous results on the dimension of Cuntz semigroups. To obtain these results, we introduce a notion of approximation for abstract Cuntz semigroups that is compatible with the approximation of a C*-algebra by sub-C*-algebras. We show that many properties for Cuntz semigroups are preserved by approximation and satisfy a Löwenheim-Skolem condition.