 

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. 


Abstract
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 CuntzPedersen 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. 

Acknowledgements
The secondnamed authour thanks NSERC (Canada) for funding.


Author information
Cristian Ivanescu:
Department of Mathematics and Statistics
Grant MacEwan University
Edmonton, Alberta, T5J 4S2, Canada
ivanescuC@macewan.ca
Dan Kucerovsky:
Department of Mathematics and Statistics
University of New Brunswick
Fredericton, New Brunswick, E3B 5A3, Canada
dkucerov@unb.ca

