Abstract
The problem of characterising those quantum logics which can be identified with the lattice of projections in a JBW-algebra or a von Neumann algebra is considered. For quantum logics which satisfy the countable chain condition and which have no TypeI 2 part, a characterisation in terms of geometric properties of the quantum state space is given.
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Communicated by H. Araki
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Bunce, L.J., Maitland Wright, J.D. Quantum logic, state space geometry and operator algebras. Commun.Math. Phys. 96, 345–348 (1984). https://doi.org/10.1007/BF01214579
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DOI: https://doi.org/10.1007/BF01214579