Siberian Mathematical Journal

, Volume 51, Issue 6, pp 971–977 | Cite as

Commutativity of projections and characterization of traces on Von Neumann algebras

Article
First Online:

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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Copyright information

© Pleiades Publishing, Ltd. 2010

Authors and Affiliations

  1. 1.Research Institute of Mathematics and Mechanics of Kazan Federal University cKazanKazanRussia

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