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arXiv · 1403.4718

Dixmier traces are weak$^*$ dense in the set of all fully symmetric traces

F. Sukochev·D. Zanin
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Abstract

We extend Dixmier's construction of singular traces (see \cite{Dixmier}) to arbitrary fully symmetric operator ideals. In fact, we show that the set of Dixmier traces is weak$^*$ dense in the set of all fully symmetric traces (that is, those traces which respect Hardy-Littlewood submajorization). Our results complement and extend earlier work of Wodzicki \cite{Wodzicki}.

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F. Sukochev, D. Zanin. 2014-03-19. Dixmier traces are weak$^*$ dense in the set of all fully symmetric traces. https://arxiv.org/abs/1403.4718

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