On the Comparison of Positive Elements of a C*-algebra by Lower Semicontinuous Traces

نویسنده

  • LEONEL ROBERT
چکیده

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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تاریخ انتشار 2008