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Mat. Zametki, 2005, Volume 77, Issue 5, Pages 727–732 (Mi mz2528)  

Connes-Dixmier Traces, Singular Symmetric Functionals, and the Notion of Connes Measurable Element

S. Lorda, A. A. Sedaevb, F. A. Sukocheva

a Flinders University
b Voronezh State Academy of Building and Architecture

Abstract: 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.

DOI: https://doi.org/10.4213/mzm2528

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English version:
Mathematical Notes, 2005, 77:5, 671–676

Bibliographic databases:

UDC: 517.51
Received: 30.06.2004

Citation: S. Lord, A. A. Sedaev, F. A. Sukochev, “Connes-Dixmier Traces, Singular Symmetric Functionals, and the Notion of Connes Measurable Element”, Mat. Zametki, 77:5 (2005), 727–732; Math. Notes, 77:5 (2005), 671–676

Citation in format AMSBIB
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