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Russian Mathematical Surveys, 2006, Volume 61, Issue 6, Pages 1039–1099
DOI: https://doi.org/10.1070/RM2006v061n06ABEH004369 (Mi rm4262) 		 
This article is cited in 45 scientific papers (total in 45 papers)

Dixmier traces and some applications in non-commutative geometry

A. L. Careya, F. A. Sukochevb

a Australian National University
b Flinders University
English version PDF (722 kB) Citations (45)
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DOI: https://doi.org/10.1070/RM2006v061n06ABEH004369
Abstract: This is a discussion of recent progress in the theory of singular traces on ideals of compact operators, with emphasis on Dixmier traces and their applications in non-commutative geometry. The starting point is the book Non-commutative geometry by Alain Connes, which contains several open problems and motivations for their solutions. A distinctive feature of the exposition is a treatment of operator ideals in general semifinite von Neumann algebras. Although many of the results presented here have already appeared in the literature, new and improved proofs are given in some cases. The reader is referred to the table of contents below for an overview of the topics considered.
Received: 10.11.2005
Russian version:
Uspekhi Matematicheskikh Nauk, 2006, Volume 61, Issue 6(372), Pages 45–110
DOI: https://doi.org/10.4213/rm4262
Bibliographic databases:
Document Type: Article
UDC: 517.98+514.7
MSC: 46L10, 58B34, 58J30, 58J42, 47L20
Language: English
Original paper language: Russian
Citation: A. L. Carey, F. A. Sukochev, “Dixmier traces and some applications in non-commutative geometry”, Uspekhi Mat. Nauk, 61:6(372) (2006), 45–110; Russian Math. Surveys, 61:6 (2006), 1039–1099
Citation in format AMSBIB
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    • This publication is cited in the following 45 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Успехи математических наук Russian Mathematical Surveys
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    Abstract page:853
    Russian version PDF:369
    English version PDF:16
    References:85
    First page:5
     
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