Hilbert lattice equations

DOI10.1007/s00023-009-0019-6zbMath1213.81022arXiv0912.1461OpenAlexW3106265123MaRDI QIDQ625073

Norman D. Megill, Mladen Pavičić

Publication date: 14 February 2011

Published in: Annales Henri Poincaré (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0912.1461

zbMATH Keywords

orthomodular latticestatevarietyprobability measureequational classGreechie diagramHilbert latticestrong set of states

Mathematics Subject Classification ID

Characterizations of Hilbert spaces (46C15) Complemented lattices, orthocomplemented lattices and posets (06C15) Logical foundations of quantum mechanics; quantum logic (quantum-theoretic aspects) (81P10) Varieties of lattices (06B20)

Related Items (3)

Quantum logic is undecidable ⋮ Kochen-Specker sets and generalized orthoarguesian equations ⋮ Graph approach to quantum systems

Cites Work

• Nonordered quantum logic and its YES-NO representation
• Varieties of orthomodular lattices related to states
• Equational bases for some varieties of orthomodular lattices related to states
• Orthomodular structures as quantum logics. Transl. from the Slovak
• Identity rule for classical and quantum theories
• Small quantum structures with small state spaces
• Equations holding in Hilbert lattices
• Varieties of Lattices
• VARIETIES OF ORTHOMODULAR LATTICES WITH A STRONGLY FULL SET OF STATES
• Vector measures on the closed subspaces of a Hilbert space
• Characterization of hilbert spaces by orthomodular spaces
• Kochen–Specker vectors
• Orthomodularity in infinite dimensions; a theorem of M. Solèr
• Quantum logic with implication
• Equations, states, and lattices of infinite-dimensional Hilbert spaces
• Algorithms for Greechie diagrams
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