A direct approach to positive normalised traces on simply generated ideals
Volume 258 / 2021
Studia Mathematica 258 (2021), 71-85
MSC: Primary 47B10, 47B37; Secondary 46B45, 46A45.
DOI: 10.4064/sm200301-24-6
Published online: 14 October 2020
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.
