2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/152321We 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 $\ell^\infty(\Bbb N)$ using tools of non standard analysis in an essential way.20 pages, AMS TeX, SFB 237-Preprint Nr.180-May 93Functional AnalysisOperator Algebrastext