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The Gleason theorem for the field of rational numbers and residue fields

Authors:	D Kh Mushtari

Institution:	(1) Research Institute of Mathematics and Mechanics, Kazan State University, USSR

Abstract:	Charges taking values in a fieldF and defined on orthomodular partially ordered sets (logics) of all projectors in some finite-dimensional linear space overF are considered. In the cases whereF is the field of rational numbers or a residue field, the Gleason representation $\mu (P) = tr(T_\mu P)$ , where $T_\mu$ is a linear operator, is proved.Translated fromMatematicheskie Zametki, Vol. 64, No. 4, pp. 584–591, October, 1998.This research was supported by the Russian Foundation for Basic Research under grant No. 96-01-01265.

Keywords:	Gleason representation linear operator trace-class operator probability measure charge orthonormal partially ordered set (logic) logic of linear projectors
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