Geodesic
Commutativity of projectors and trace characterization on von Neumann algebras.~I
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 12 (2009), pp. 80-83

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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. 
@article{IVM_2009_12_a9,
     author = {A. M. Bikchentaev},
     title = {Commutativity of projectors and trace characterization on von {Neumann} {algebras.~I}},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {80--83},
     publisher = {mathdoc},
     number = {12},
     year = {2009},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2009_12_a9/}
}
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A. M. Bikchentaev. Commutativity of projectors and trace characterization on von Neumann algebras.~I. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 12 (2009), pp. 80-83. http://geodesic.mathdoc.fr/item/IVM_2009_12_a9/