Sibirskii Matematicheskii Zhurnal
RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
General information
Latest issue
Archive
Impact factor

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Sibirsk. Mat. Zh.:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


Sibirskii Matematicheskii Zhurnal, 2005, Volume 46, Number 1, Pages 32–45 (Mi smj956)  

This article is cited in 19 scientific papers (total in 19 papers)

On representation of elements of a Von Neumann algebra in the form of finite sums of products of projections

A. M. Bikchentaev

N. G. Chebotarev Research Institute of Mathematics and Mechanics, Kazan State University
References:
Abstract: We prove that each element of the von Neumann algebra without a direct abelian summand is representable as a finite sum of products of at most three projections in the algebra. In a properly infinite algebra the number of product terms is at most two. Our result gives a new proof of equivalence of the primary classification of von Neumann algebras in terms of projections and traces and also a description for the Jordan structure of the “algebra of observables” of quantum mechanics in terms of the “questions” of quantum mechanics.
Keywords: $C^*$-algebra, von Neumann algebra, trace, bounded linear operator, idempotent, projection, linear span, Hilbert space.
Received: 02.04.2004
English version:
Siberian Mathematical Journal, 2005, Volume 46, Issue 1, Pages 24–34
DOI: https://doi.org/10.1007/s11202-005-0003-4
Bibliographic databases:
UDC: 517.983, 517.986
Language: Russian
Citation: A. M. Bikchentaev, “On representation of elements of a Von Neumann algebra in the form of finite sums of products of projections”, Sibirsk. Mat. Zh., 46:1 (2005), 32–45; Siberian Math. J., 46:1 (2005), 24–34
Citation in format AMSBIB
\Bibitem{Bik05}
\by A.~M.~Bikchentaev
\paper On representation of elements of a~Von~Neumann algebra in the form of finite sums of products of projections
\jour Sibirsk. Mat. Zh.
\yr 2005
\vol 46
\issue 1
\pages 32--45
\mathnet{http://mi.mathnet.ru/smj956}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2141300}
\zmath{https://zbmath.org/?q=an:1106.46045}
\transl
\jour Siberian Math. J.
\yr 2005
\vol 46
\issue 1
\pages 24--34
\crossref{https://doi.org/10.1007/s11202-005-0003-4}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000227076100003}
Linking options:
  • https://www.mathnet.ru/eng/smj956
  • https://www.mathnet.ru/eng/smj/v46/i1/p32
  • This publication is cited in the following 19 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
    Statistics & downloads:
    Abstract page:1503
    Full-text PDF :857
    References:384
     
      Contact us:
     Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2024