Browsing by Author "Ivanescu, Cristian"
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Item Cu-nuclearity implies LLP and exactness(2021) Ivanescu, Cristian; Kucerovsky, DanThe Cu-nuclearity property is an analogue of Skandalis's notion of K-nuclearity, adapted to the case of Cuntz semigroups of C*-algebras. We prove that this implies nuclearity, and we introduce a weaker form of the condition. We prove that the new condition weak Cu-nuclearity, for simple separable C*-algebras, implies exactness and the local lifting property (LLP). We also prove that if A is a simple C*-algebra with the weak Cu-nuclearity property, and B is any simple C*-algebra, then A ⊗min B = A ⊗max B. We prove that Cu-nuclearity does imply nuclearity, and that in some cases this is also true for weak Cu-nuclearity.Item Traces and Pedersen ideals of tensor products of non-unital C*-algebras(2019) Ivanescu, Cristian; Kucerovsky, DanWe show that positive elements of a Pedersen ideal of a tensor product can be approximated in a particularly strong sense by sums of tensor products of positive elements. This has a range of applications to the structure of tracial cones and related topics, such as the Cuntz-Pedersen space or the Cuntz semigroup. For example, we determine the cone of lower semicontinuous traces of a tensor product in terms of the traces of the tensor factors, in an arbitrary C*-tensor norm. We show that the positive elements of a Pedersen ideal are sometimes stable under Cuntz equivalence. We generalize a result of Pedersen’s by showing that certain classes of completely positive maps take a Pedersen ideal into a Pedersen ideal. We provide theorems that in many cases compute the Cuntz semigroup of a tensor product.