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Mat. Zametki, 2011, Volume 89, Issue 4, Pages 483–494 (Mi mz8640)  

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

Commutation of Projections and Trace Characterization on von Neumann Algebras. II

A. M. Bikchentaev

Kazan (Volga Region) Federal University

Abstract: We obtain new necessary and sufficient commutation conditions for projections in terms of operator inequalities. These inequalities are applied for trace characterization on von Neumann algebras for the class of all positive normal functionals.

Keywords: projection, von Neumann algebra, Hilbert space, trace, commutation of operators, normal functional, linear bounded operator, operator inequality

DOI: https://doi.org/10.4213/mzm8640

Full text: PDF file (501 kB)
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English version:
Mathematical Notes, 2011, 89:4, 461–471

Bibliographic databases:

UDC: 517.986
Received: 23.06.2009
Revised: 22.04.2010

Citation: A. M. Bikchentaev, “Commutation of Projections and Trace Characterization on von Neumann Algebras. II”, Mat. Zametki, 89:4 (2011), 483–494; Math. Notes, 89:4 (2011), 461–471

Citation in format AMSBIB
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\pages 461--471
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    This publication is cited in the following articles:
    1. 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
    2. 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
    3. 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
    4. 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
    5. Bikchentaev A., “Integrable products of measurable operators”, Lobachevskii J. Math., 37:4, SI (2016), 397–403  crossref  mathscinet  zmath  isi  elib  scopus
    6. Bikchentaev A.M., “Trace and integrable operators affiliated with a semifinite von Neumann algebra”, Dokl. Math., 93:1 (2016), 16–19  crossref  mathscinet  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 and the quantum Hall effect”, Theoret. and Math. Phys., 195:1 (2018), 557–562  mathnet  crossref  crossref  adsnasa  isi  elib
    9. Abed S.A., “An Inequality For Projections and Convex Functions”, Lobachevskii J. Math., 39:9 (2018), 1287–1292  crossref  mathscinet  zmath  isi  scopus
    10. A. M. Bikchentaev, “Metriki na proektorakh algebry fon Neimana, assotsiirovannye so sledovymi funktsionalami”, Sib. matem. zhurn., 60:6 (2019), 1223–1228  mathnet  crossref
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