Traces and Pedersen ideals of tensor products of non-unital C*-algebras

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dc.contributor.authorIvanescu, Cristian
dc.contributor.authorKucerovski, Dan
dc.date.accessioned2020-10-30
dc.date.accessioned2022-05-31T01:16:06Z
dc.date.available2022-05-31T01:16:06Z
dc.date.issued2019
dc.description.abstractWe 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.
dc.format.extent295.79KB
dc.format.mimetypePDF
dc.identifier.citationIvanescu, C. and Kucerovski, D. (2019). Traces and Pedersen ideals of tensor products of non-unital C*-algebras. New York Journal of Mathematics, 25, 423-450. https://arxiv.org/abs/1811.04430v2
dc.identifier.urihttps://hdl.handle.net/20.500.14078/1979
dc.languageEnglish
dc.language.isoen
dc.rightsAll Rights Reserved
dc.subjectC ∗ -algebra
dc.subjecttensor product
dc.titleTraces and Pedersen ideals of tensor products of non-unital C*-algebras
dc.typeArticle
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