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Symmetry, Integrability and Geometry: Methods and Applications, 2010, Volume 6, 072, 36 pp.
DOI: https://doi.org/10.3842/SIGMA.2010.072 (Mi sigma530) 		 
This article is cited in 8 scientific papers (total in 8 papers)

Measure Theory in Noncommutative Spaces

Steven Lorda, Fedor Sukochevb

a School of Mathematical Sciences, University of Adelaide, Adelaide, 5005, Australia
b University of New South Wales, School of Mathematics and Statistics
Full-text PDF (516 kB) Citations (8)
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DOI: https://doi.org/10.3842/SIGMA.2010.072
Abstract: The integral in noncommutative geometry (NCG) involves a non-standard trace called a Dixmier trace. The geometric origins of this integral are well known. From a measure-theoretic view, however, the formulation contains several difficulties. We review results concerning the technical features of the integral in NCG and some outstanding problems in this area. The review is aimed for the general user of NCG.
Keywords: Dixmier trace; singular trace; noncommutative integration; noncommutative geometry; Lebesgue integral; noncommutative residue.
Received: March 25, 2010; in final form August 4, 2010; Published online September 16, 2010
Bibliographic databases:
Document Type: Article
MSC: 46L51; 47B10; 58B34
Language: English
Citation: Steven Lord, Fedor Sukochev, “Measure Theory in Noncommutative Spaces”, SIGMA, 6 (2010), 072, 36 pp.
Citation in format AMSBIB
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\by Steven Lord, Fedor Sukochev
\paper Measure Theory in Noncommutative Spaces
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\papernumber 072
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    • This publication is cited in the following 8 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Symmetry, Integrability and Geometry: Methods and Applications
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