Smearing of Observables and Spectral Measures on Quantum Structures

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.

References in corpus (4)

• Sharp and fuzzy observables on effect algebras
• Blocks of homogeneous effect algebras
• Representation of States on Effect-Tribes and Effect Algebras by Integrals
• Observables on Quantum Structures