Measure Theory in Noncommutative Spaces
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...
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| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Datum: | 2010 |
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| Format: | Artikel |
| Sprache: | English |
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Інститут математики НАН України
2010
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/146508 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | Measure Theory in Noncommutative Spaces / S. Lord, F. Sukochev // Symmetry, Integrability and Geometry: Methods and Applications. — 2010. — Т. 6. — Бібліогр.: 75 назв. — англ. |
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Lord, S. Sukochev, F. 2019-02-09T19:36:57Z 2019-02-09T19:36:57Z 2010 Measure Theory in Noncommutative Spaces / S. Lord, F. Sukochev // Symmetry, Integrability and Geometry: Methods and Applications. — 2010. — Т. 6. — Бібліогр.: 75 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 46L51; 47B10; 58B34 DOI:10.3842/SIGMA.2010.072 https://nasplib.isofts.kiev.ua/handle/123456789/146508 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. This paper is a contribution to the Special Issue “Noncommutative Spaces and Fields”. The full collection is available at http://www.emis.de/journals/SIGMA/noncommutative.html. The authors thank N. Kalton for many discussions concerning Dixmier traces and symmetric functionals. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Measure Theory in Noncommutative Spaces Article published earlier |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| title |
Measure Theory in Noncommutative Spaces |
| spellingShingle |
Measure Theory in Noncommutative Spaces Lord, S. Sukochev, F. |
| title_short |
Measure Theory in Noncommutative Spaces |
| title_full |
Measure Theory in Noncommutative Spaces |
| title_fullStr |
Measure Theory in Noncommutative Spaces |
| title_full_unstemmed |
Measure Theory in Noncommutative Spaces |
| title_sort |
measure theory in noncommutative spaces |
| author |
Lord, S. Sukochev, F. |
| author_facet |
Lord, S. Sukochev, F. |
| publishDate |
2010 |
| language |
English |
| container_title |
Symmetry, Integrability and Geometry: Methods and Applications |
| publisher |
Інститут математики НАН України |
| format |
Article |
| description |
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.
|
| issn |
1815-0659 |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/146508 |
| citation_txt |
Measure Theory in Noncommutative Spaces / S. Lord, F. Sukochev // Symmetry, Integrability and Geometry: Methods and Applications. — 2010. — Т. 6. — Бібліогр.: 75 назв. — англ. |
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2025-12-07T19:40:39Z |
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2025-12-07T19:40:39Z |
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1850879706802421760 |