Quantum measures and states on Jordan algebras

DOI10.1007/BF01220507zbMath0579.46049OpenAlexW2028498782MaRDI QIDQ1067180

J. D. Maitland Wright, Leslie J. Bunce

Publication date: 1985

Published in: Communications in Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf01220507

zbMATH Keywords

quantum logicfoundations of quantum mechanicsJordan productbounded observablesGleason's theoremcomplete orthomodular latticeextend the Gleason- Christensen-Yeadon theorem from von Neumann algebras to JBW-algebrasJordan algebra of self-adjoint operators

Mathematics Subject Classification ID

Selfadjoint operator algebras ((C^*)-algebras, von Neumann ((W^*)-) algebras, etc.) (46L99) Free probability and free operator algebras (46L54) Noncommutative probability and statistics (46L53) Noncommutative measure and integration (46L51) Logical foundations of quantum mechanics; quantum logic (quantum-theoretic aspects) (81P10) States of selfadjoint operator algebras (46L30) Jordan structures on Banach spaces and algebras (17C65)

Related Items (17)

Quantum logics and convex geometry ⋮ The connection between the universal enveloping C*-algebra and the universal enveloping von Neumann algebra of a JW-algebra ⋮ The Mackey-Gleason Problem ⋮ Spectral order of operators and range projections ⋮ Gleason’s theorem for composite systems ⋮ An approach to quantum mechanics via conditional probabilities ⋮ On two problems concerning enveloping von Neumann algebras of JW-algebras ⋮ Measures on the quantum logic of subspaces of a \(J\)-space ⋮ Star order on JBW algebras ⋮ Bibliography on quantum logics and related structures ⋮ A simple and quantum-mechanically motivated characterization of the formally real Jordan algebras ⋮ Local tomography and the role of the complex numbers in quantum mechanics ⋮ A representation of quantum measurement in order-unit spaces ⋮ Unnamed Item ⋮ Dye's theorem for tripotents in von Neumann algebras and JBW\(^*\)-triples ⋮ Quasi-states and quasi-measures ⋮ Quantum logic, state space geometry and operator algebras

Cites Work

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• TYPE I₂ JBW-ALGEBRAS
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• Quantum Mechanics and Hilbert Space
• Jordan algebras of self-adjoint operators
• Irreducible Jordan Algebras of Self-Adjoint Operators
• Jordan Algebras of Self-Adjoint Operators
• Measures and Tensors
• Quasi-States on C ∗ -Algebras

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