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

Leonel Robert

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arXiv · 0806.1570

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

Leonel Robert

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Abstract

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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Leonel Robert. 2008-06-10. On the comparison of positive elements of a C*-algebra by lower semicontinuous traces. https://arxiv.org/abs/0806.1570

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