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On the distinction between the classes of Dixmier and Connes-Dixmier traces (1210.3397v1)
Published 11 Oct 2012 in math.OA and math.FA
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.