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Sibirskii Matematicheskii Zhurnal, 2010, Volume 51, Number 6, Pages 1228–1236 (Mi smj2157)  
This article is cited in 23 scientific papers (total in 23 papers)

Commutativity of projections and characterization of traces on von Neumann algebras

A. M. Bikchentaev

N. G. Chebotarev Research Institute of Mathematics and Mechanics, Kazan State University, Kazan
Full-text PDF (320 kB) Citations (23)
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Abstract: We find new necessary and sufficient conditions for the commutativity of projections in terms of operator inequalities. We apply these inequalities to characterize a trace on von Neumann algebras in the class of all positive normal functionals. We obtain some characterization of a trace on von Neumann algebras in terms of the commutativity of products of projections under a weight.
Keywords: Hilbert space, von Neumann algebra, spectral theorem, weight, trace, normal functional, bounded linear operator, projection, operator inequality, commutativity of operators.
Received: 03.06.2009
English version:
Siberian Mathematical Journal, 2010, Volume 51, Issue 6, Pages 971–977
DOI: https://doi.org/10.1007/s11202-010-0096-2
Bibliographic databases:
Document Type: Article
UDC: 517.983+517.986
Language: Russian
Citation: A. M. Bikchentaev, “Commutativity of projections and characterization of traces on von Neumann algebras”, Sibirsk. Mat. Zh., 51:6 (2010), 1228–1236; Siberian Math. J., 51:6 (2010), 971–977
Citation in format AMSBIB
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    • This publication is cited in the following 23 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Сибирский математический журнал Siberian Mathematical Journal
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