%0 Journal Article %T Dixmier traces are weak$^*$ dense in the set of all fully symmetric traces %A F. Sukochev %A D. Zanin %J Mathematics %D 2014 %I arXiv %X 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}. %U http://arxiv.org/abs/1403.4718v1