Geodesic
Connes-Dixmier Traces, Singular Symmetric Functionals, and the Notion of Connes Measurable Element
Matematičeskie zametki, Tome 77 (2005) no. 5, pp. 727-732

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This paper continues the study started in [1–5]. We show that the construction of abnormal traces used in [1, 2] can adequately be expressed by using the construction of singular symmetric functionals developed in [4, 5]. We completely describe the measurable elements on which all singular symmetric functionals from a certain class take the same values [1]. This result significantly complements the description of the structure of the set of measurable operators even in the special case studied in [1]. For natural subsets of the set of singular symmetric functionals, we obtain new results concerning their normalization properties. 
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     author = {S. Lord and A. A. Sedaev and F. A. Sukochev},
     title = {Connes-Dixmier {Traces,} {Singular} {Symmetric} {Functionals,} and the {Notion} of {Connes} {Measurable} {Element}},
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S. Lord; A. A. Sedaev; F. A. Sukochev. Connes-Dixmier Traces, Singular Symmetric Functionals, and the Notion of Connes Measurable Element. Matematičeskie zametki, Tome 77 (2005) no. 5, pp. 727-732. http://geodesic.mathdoc.fr/item/MZM_2005_77_5_a6/