Lifting, \(n\)-dimensional spectral resolutions, and \(n\)-dimensional observables

DOI10.1007/s00012-020-00664-8zbMath1471.06006arXiv2002.08280OpenAlexW3033651844MaRDI QIDQ776988

Anatolij Dvurečenskij, Dominik Lachman

Publication date: 13 July 2020

Published in: Algebra Universalis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2002.08280

zbMATH Keywords

tribeliftingMV-algebraeffect algebraeffect-tribeunital po-groupLoomis-Sikorski theoremjoint observable\(n\)-dimensional observable\(n\)-dimensional spectral resolution

Mathematics Subject Classification ID

Logical foundations of quantum mechanics; quantum logic (quantum-theoretic aspects) (81P10) MV-algebras (06D35) Ordered abelian groups, Riesz groups, ordered linear spaces (06F20)

Related Items

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, Sum of \(n\)-dimensional observables on MV-effect algebras

Cites Work

• Effect algebras and unsharp quantum logics.
• 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
• Observables on lexicographic effect algebras
• Two-dimensional observables and spectral resolutions
• Observables on perfect MV-algebras
• Loomis-Sikorski representation of monotone \(\sigma\)-complete effect algebras
• Orthomodular lattices admitting no states
• On a Theorem of Von Neumann
• Foundations of Modern Probability
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item