Geodesic
Connes-Dixmier Traces, Singular Symmetric Functionals, and the Notion of Connes Measurable Element
Matematičeskie zametki, Tome 77 (2005) no. 5, pp. 727-732 
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/
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Voir la notice de l'article provenant de la source Math-Net.Ru

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.

[1] Connes A., Noncommutative Geometry, Academic Press, San Diego, 1994 | Zbl

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[3] Dodds P., de Pagter B., Semenov E., Sukochev F., “Symmetric functionals and singular traces”, Positivity, 2 (1998), 47–75 | DOI | MR | Zbl

[4] Dodds P. G., de Pagter B., Sedaev A. A., Semenov E. M., Sukochev F. A., “Singulyarnye simmetrichnye funktsionaly”, Zapiski nauch. sem. POMI, 290, POMI, SPb., 2002, 42–71 | Zbl

[5] Dodds P. G., de Pagter B., Sedaev A. A., Semenov E. M., Sukochev F. A., “Singulyarnye simmetrichnye funktsionaly i banakhovy predely s dopolnitelnymi svoistvami invariantnosti”, Izv. AN. Ser. matem., 67:6 (2003), 111–136 | MR | Zbl

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