Rings with effects

D. J. Foulis

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arXiv · quant-ph/0609181

Rings with effects

D. J. Foulis

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Abstract

A ring with effects (e-ring) is a generalization of the ring of bounded linear operators on a Hilbert space and the subsystem of effect operators (positive Hermitian operators dominated by the identity operator). The POV-measures representing (perhaps fuzzy) quantum mechanical observables take on their valued in the system of Hilbert-space effect operators. We study and give several examples of e-rings, including von Neumann algebras and rings of bounded measurable functions.

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D. J. Foulis. 2006-09-23. Rings with effects. https://arxiv.org/abs/quant-ph/0609181

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