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Sibirsk. Mat. Zh., 2010, Volume 51, Number 6, Pages 1228–1236 (Mi smj2157)  

This article is cited in 10 scientific papers (total in 10 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

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.

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English version:
Siberian Mathematical Journal, 2010, 51:6, 971–977

Bibliographic databases:

Document Type: Article
UDC: 517.983+517.986
Received: 03.06.2009

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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\pages 971--977
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Dinh Trung Hoa, Osaka H., Ho Minh Toan, “On Generalized Powers-Stormer's Inequality”, Linear Alg. Appl., 438:1 (2013), 242–249  crossref  mathscinet  zmath  isi  scopus
    2. Bikchentaev A.M., “Commutativity of Operators and Characterization of Traces on $C^{*}$-Algebras”, Dokl. Math., 87:1 (2013), 79–82  crossref  crossref  mathscinet  zmath  isi  elib  elib  scopus
    3. D. Dauitbek, N. E. Tokmagambetov, K. S. Tulenov, “Commutator inequalities associated with polar decompositions of $\tau$-measurable operators”, Russian Math. (Iz. VUZ), 58:7 (2014), 48–52  mathnet  crossref
    4. Bikchentaev A.M., “Commutation of Projections and Characterization of Traces on Von Neumann Algebras. III”, Int. J. Theor. Phys., 54:12 (2015), 4482–4493  crossref  mathscinet  zmath  isi  elib  scopus
    5. A. M. Bikchentaev, “Inequality for a Trace on a Unital $C^*$-Algebra”, Math. Notes, 99:4 (2016), 487–491  mathnet  crossref  crossref  mathscinet  isi  elib
    6. Bikchentaev A.M., “Trace and Integrable Operators Affiliated With a Semifinite Von Neumann Algebra”, Dokl. Math., 93:1 (2016), 16–19  crossref  zmath  isi  elib  scopus
    7. Bikchentaev A.M., “On Tau-Compactness of Products of Tau-Measurable Operators”, Int. J. Theor. Phys., 56:12 (2017), 3819–3830  crossref  mathscinet  zmath  isi  scopus
    8. A. M. Bikchentaev, “Differences of idempotents in $C^*$-algebras”, Siberian Math. J., 58:2 (2017), 183–189  mathnet  crossref  crossref  isi  elib  elib
    9. A. M. Bikchentaev, “Differences of idempotents in $C^*$-algebras and the quantum Hall effect”, Theoret. and Math. Phys., 195:1 (2018), 557–562  mathnet  crossref  crossref  adsnasa  isi  elib
    10. A. M. Bikchentaev, “Sled i raznosti idempotentov v $C^*$-algebrakh”, Matem. zametki, 105:5 (2019), 647–655  mathnet  crossref  elib
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