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arXiv · 1210.3397

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

Fedor Sukochev·Alexandr Usachev·Dmitriy Zanin
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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.

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Fedor Sukochev, Alexandr Usachev, Dmitriy Zanin. 2012-10-11. On the distinction between the classes of Dixmier and Connes-Dixmier traces. https://arxiv.org/abs/1210.3397

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