On Characterizing the Standard Quantum Logics

DOI10.2307/1997836zbMath0366.06019OpenAlexW4249000959MaRDI QIDQ4141870

John W. Wilbur

Publication date: 1977

Full work available at URL: https://doi.org/10.2307/1997836

Mathematics Subject Classification ID

Hilbert and pre-Hilbert spaces: geometry and topology (including spaces with semidefinite inner product) (46C05) Representations of topological algebras with involution (46K10) Structure and representation theory of distributive lattices (06D05) Complemented lattices, orthocomplemented lattices and posets (06C15) Quadratic and bilinear forms, inner products (15A63) Modular lattices, Desarguesian lattices (06C05) Analytic and descriptive geometry (51N99) Miscellaneous applications of functional analysis (46N99) Ordered fields (12J15) General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to ordered structures (06-00)

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Cites Work

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• Locally compact division rings
• Remarks on type I Baer and Baer\(^*\)-rings
• Zur Begründung der projektiven Geometrie
• Axioms for non-relativistic quantum mechanics
• On the lattice of closed subspaces of Hilbert spaces
• The logic of quantum mechanics
• Observables and the Field in Quantum Mechanics
• Quantum Logic and the Locally Convex Spaces
• The Orthomodular Identity and Metric Completeness of the Coordinatizing Division Ring
• Vector space models of abstract quantum logics