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Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2009, Number 12, Pages 80–83 (Mi ivm6028)  
This article is cited in 4 scientific papers (total in 4 papers)

Brief communications

Commutativity of projectors and trace characterization on von Neumann algebras. I

A. M. Bikchentaev

Research Institute of Mathematics and Mechanics, Kazan State University, Kazan, Russia
Full-text PDF (160 kB) Citations (4)
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Abstract: We obtain the necessary and sufficient conditions for commutativity of projectors in terms of operator inequalities. We apply these conditions for the trace characterization on von Neumann algebras in the class of all positive normal functionals.
We also characterize the trace on von Neumann algebras in terms of commutation of projectors under the weight sign.
Keywords: Hilbert space, von Neumann algebra, spectral theorem, weight, trace, normal functional, linear bounded operator, projector, operator inequality, commutativity of operators.
Received: 04.06.2009
English version:
Russian Mathematics (Izvestiya VUZ. Matematika), 2009, Volume 53, Issue 12, Pages 68–71
DOI: https://doi.org/10.3103/S1066369X0912010X
Bibliographic databases:
Document Type: Article
UDC: 517.983+517.986
Language: Russian
Citation: A. M. Bikchentaev, “Commutativity of projectors and trace characterization on von Neumann algebras. I”, Izv. Vyssh. Uchebn. Zaved. Mat., 2009, no. 12, 80–83; Russian Math. (Iz. VUZ), 53:12 (2009), 68–71
Citation in format AMSBIB
\Bibitem{Bik09}
\by A.~M.~Bikchentaev
\paper Commutativity of projectors and trace characterization on von Neumann algebras.~I
\jour Izv. Vyssh. Uchebn. Zaved. Mat.
\yr 2009
\issue 12
\pages 80--83
\mathnet{http://mi.mathnet.ru/ivm6028}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2664476}
\zmath{https://zbmath.org/?q=an:1188.46038}
\transl
\jour Russian Math. (Iz. VUZ)
\yr 2009
\vol 53
\issue 12
\pages 68--71
\crossref{https://doi.org/10.3103/S1066369X0912010X}
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  • https://www.mathnet.ru/eng/ivm/y2009/i12/p80
    Cycle of papers
    This publication is cited in the following 4 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Известия высших учебных заведений. Математика Russian Mathematics (Izvestiya VUZ. Matematika)
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