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arXiv · 1204.6486

Smearing of Observables and Spectral Measures on Quantum Structures

Anatolij Dvurečenskij
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Abstract

An observable on a quantum structure is any $\sigma$-homomorphism of quantum structures from the Borel $\sigma$-algebra of the real line into the quantum structure which is in our case a monotone $\sigma$-complete effect algebras with the Riesz Decomposition Property. We show that every observable is a smearing of a sharp observable which takes values from a Boolean $\sigma$-subalgebra of the effect algebra, and we prove that for every element of the effect algebra there is its spectral measure.

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Anatolij Dvurečenskij. 2012-04-29. Smearing of Observables and Spectral Measures on Quantum Structures. https://doi.org/10.1007/s10701-012-9689-x

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