On the distinction between the classes of Dixmier and Connes-Dixmier traces

Abstract

In the present paper we prove that the classes of Dixmier and Connes-Dixmier traces differ even on the Dixmier ideal ${\mathcal{M}}_{1,\infty }$. We construct a Marcinkiewicz space ${\mathcal{M}}_{\psi }$ and a positive operator $T\in {\mathcal{M}}_{\psi }$ which is Connes-Dixmier measurable but which is not Dixmier measurable.

References in corpus (1)

• Measure Theory in Noncommutative Spaces