On the comparison of positive elements of a C*-algebra by lower semicontinuous traces Leonel Robert 46L0546L35positive elementslower semicontinuous traces 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. Indiana University Mathematics Journal 2009 text pdf 10.1512/iumj.2009.58.3704 10.1512/iumj.2009.58.3704 en Indiana Univ. Math. J. 58 (2009) 2509 - 2516 state-of-the-art mathematics http://iumj.org/access/