A direct approach to positive normalised traces on simply generated ideals

Abstract

We present a construction of positive normalised singular traces on a wide class of principal ideals. The feature of our approach is a direct application of Hahn-Banach theorem on the level of traces. This allows us to avoid the mediation of some extended limiting functionals, used in the classical work of J. Dixmier. n k=0 a k (A) , 0 ≤ A ∈ M ψ ,