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

Sukochev, Fedor; Usachev, Alexandr; Zanin, Dmitriy

doi:10.1090/S0002-9939-2012-11853-2

On the distinction between the classes of Dixmier and Connes-Dixmier traces
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by Fedor Sukochev, Alexandr Usachev and Dmitriy Zanin PDF

Proc. Amer. Math. Soc. 141 (2013), 2169-2179 Request permission

Abstract:

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.

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