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Commutativity of projections and characterization of traces on Von Neumann algebras

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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.

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Authors and Affiliations

  1. Research Institute of Mathematics and Mechanics of Kazan Federal University cKazan, Kazan, Russia

    A.M. Bikchentaev

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  1. A.M. Bikchentaev
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Correspondence to A.M. Bikchentaev.

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Translated from Sibirskii Matematicheskii Zhurnal, Vol. 51, No. 6, pp. 1201–1214, November–December

Original Russian Text Copyright © 2010 Bikchentaev A. M.

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Bikchentaev, A. Commutativity of projections and characterization of traces on Von Neumann algebras. Sib Math J 51, 971–977 (2010). https://doi.org/10.1007/s11202-010-0096-2

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