New York Journal of Mathematics
Volume 25 (2019), 423-450


Cristian Ivanescu and Dan Kucerovsky

Traces and Pedersen ideals of tensor products of nonunital C*-algebras

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Published: May 25, 2019.
Keywords: C*-algebra, tensor product.
Subject: Primary 46A32, 46L06; Secondary 47L07, 47L50.

We 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.


The second-named authour thanks NSERC (Canada) for funding.

Author information

Cristian Ivanescu:
Department of Mathematics and Statistics
Grant MacEwan University
Edmonton, Alberta, T5J 4S2, Canada


Dan Kucerovsky:
Department of Mathematics and Statistics
University of New Brunswick
Fredericton, New Brunswick, E3B 5A3, Canada