We give a necessary and sufficient condition on a positive compact operator T for the existence of a singular trace (i.e. a trace vanishing on the finite rank operators) which takes a finite non-zero value on T. This generalizes previous results by Dixmier and Varga. We also give an explicit description of these traces and associated ergodic states on l(infinity)(N) using tools of non standard analysis in an essential way. (C) 1996 Academic Press, Inc.
Albeverio, S., Guido, D., Ponosov, A., Scarlatti, S. (1996). Singular traces and compact operators. JOURNAL OF FUNCTIONAL ANALYSIS, 137(2), 281-302 [10.1006/jfan.1996.0047].