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

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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.

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Authors and Affiliations

  1. School of Informatics and Engineering, Flinders University of South Australia, Australia

    S. Lord & F. A. Sukochev

  2. Voronezh State Architecture and Civil Engineering University, Voronezh, Russia

    A. A. Sedaev

Authors
  1. S. Lord
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  2. A. A. Sedaev
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  3. F. A. Sukochev
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__________

Translated from Matematicheskie Zametki, vol. 77, no. 5, 2005, pp. 727–732.

Original Russian Text Copyright ©2005 by S. Lord, A. A. Sedaev, F. A. Sukochev.

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Lord, S., Sedaev, A.A. & Sukochev, F.A. Connes-Dixmier Traces, Singular Symmetric Functionals, and the Notion of Connes Measurable Element. Math Notes 77, 671–676 (2005). https://doi.org/10.1007/s11006-005-0067-2

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  • DOI: https://doi.org/10.1007/s11006-005-0067-2

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