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

Authors: Leonel Robert

Issue: Volume 58 (2009), Issue 6, 2509-2516

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.