Quantum logics and convex geometry
type: Item
instance of: scholarly article
title: Quantum logics and convex geometry
zbMATH Open document ID: 0602.03018
DOI: 10.1007/BF01212357
author: J. D. Maitland Wright
author: Leslie J. Bunce
published in: Communications in Mathematical Physics
publication date: 1985-01-01T00:00:00Z
review text: It has been of considerable interest to characterize among quantum logics \((=complete\) orthomodular lattices) such ones being representable in terms of more familiar entities like the projection lattices of von Neumann algebras. Atomic lattices have been thoroughly investigated, while the authors previously succeeded in characterizing quantum logics representable as the projection lattices of von Neumann algebras or JBW- algebras subject to certain countability conditions [Commun. Math. Phys. 96, 345-348 (1984; Zbl 0586.03049)]. The main result of this paper is that a large class of quantum logics may be identified with lattices of projections arising naturally in certain convex sets, which enabled the authors to extend their earlier results.
Mathematics Subject Classification ID: 03G12
Mathematics Subject Classification ID: 52C07
Mathematics Subject Classification ID: 06C15
zbMATH DE Number: 3970747
zbMATH Keywords: complete orthomodular lattices
zbMATH Keywords: von Neumann algebras
zbMATH Keywords: projection lattices
zbMATH Keywords: JBW-algebras
reviewed by: Hirokazu Nishimura
MaRDI profile type: Publication
cites work: Non-commutative spectral theory for affine function spaces on convex sets
cites work: On Non-Commutative Spectral Theory and Jordan Algebras
cites work: Quantum measures and states on Jordan algebras
cites work: Quantum logic, state space geometry and operator algebras
cites work: Measures on projections and physical states
cites work: Normal state spaces of Jordan and von Neumann algebras
cites work: Jordan-Hahn decomposition of signed weights on finite orthogonality spaces
cites work: On Characterizing the Standard Quantum Logics
cites work: Measures on Projections in W*-algebras of Type II1
cites work: Axioms for non-relativistic quantum mechanics
Recommended article: Quantum logics and convex spaces
Recommended article: Convexity and finite quantum logics
Recommended article: Convex quantum logic
Recommended article: Quantum logic and non-commutative geometry
Recommended article: Q4530837
Recommended article: Quantum logic, state space geometry and operator algebras
Recommended article: Quantum logics and Hilbert space
Recommended article: Geometrical models for quantum logics with conditioning
Recommended article: Q4713118
Recommended article: Concrete quantum logics
description: scientific article; zbMATH DE number 3970747