Two-dimensional observables and spectral resolutions

DOI10.1016/S0034-4877(20)30023-9zbMath1441.81004OpenAlexW3016412991MaRDI QIDQ2194280

Dominik Lachman, Anatolij Dvurečenskij

Publication date: 25 August 2020

Published in: Reports on Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s0034-4877(20)30023-9

zbMATH Keywords

tribeobservablestateMV-algebraeffect algebraeffect-tribeLoomis-Sikorski theoremtwo-dimensional observabletwo-dimensional spectral resolution

Mathematics Subject Classification ID

Classes of sets (Borel fields, (sigma)-rings, etc.), measurable sets, Suslin sets, analytic sets (28A05) Logical foundations of quantum mechanics; quantum logic (quantum-theoretic aspects) (81P10) MV-algebras (06D35)

Related Items (5)

Homogeneous effect algebras and observables vs spectral resolutions ⋮ \(n\)-dimensional observables on \(k\)-perfect MV-algebras and \(k\)-perfect effect algebras. I: Characteristic points ⋮ \(n\)-dimensional observables on \(k\)-perfect MV-algebras and \(k\)-perfect effect algebras. II: One-to-one correspondence ⋮ Spectral resolutions and quantum observables ⋮ Lifting, \(n\)-dimensional spectral resolutions, and \(n\)-dimensional observables

Cites Work

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• Effect algebras and unsharp quantum logics.
• On orders of observables on effect algebras
• Observables on quantum structures
• Interpretation of AF \(C^*\)-algebras in Łukasiewicz sentential calculus
• Tensor products and the Loomis-Sikorski theorem for MV-algebras
• Generalization of blocks for \(D\)-lattices and lattice-ordered effect algebras
• Algebraic foundations of many-valued reasoning
• The spectrum of the sum of observables on \(\sigma\)-complete MV-effect algebras
• Observables on perfect MV-algebras
• Loomis-Sikorski representation of monotone \(\sigma\)-complete effect algebras
• Orthomodular lattices admitting no states
• Foundations of Modern Probability
• Central elements and Cantor-Bernstein's theorem for pseudo-effect algebras
• Compatibility and decompositions of effects
• Pseudoeffect algebras. I: Basic properties
• MV-observables and MV-algebras
• Effect algebras which can be covered by MV-algebras

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