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

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