Dixmier traces are weak${}^{\ast }$ dense in the set of all fully symmetric traces

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${}^{\ast }$ 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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