On the comparison of positive elements of a C*-algebra by lower semicontinuous traces

Details On the comparison of positive elements of a C*-algebra by lower semicontinuous traces On the comparison of positive elements of a C*-algebra by lower semicontinuous traces

2008-06-10

arxiv.org/abs/0806.1570v1

Mathematics

Operator Algebras

5 pages; submitted for publication

Scientific paper

It is shown in this paper that two positive elements of a C*-algebra agree on all lower semicontinuous traces if and only if they are equivalent in the sense of Cuntz and Pedersen. A similar result is also obtained in the more general case where the two elements are comparable by their values on the lower semicontinuous traces. This result is used to give a characterization of the functions on the cone of lower semicontinuous traces of a stable C*-algebra that arise from positive elements of the algebra.

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