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Quantum logics and convex geometry

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Abstract

The main result is a representation theorem which shows that, for a large class of quantum logics, a quantum logic,Q, is isomorphic to the lattice of projective faces in a suitable convex setK. As an application we extend our earlier results [4], which, subject to countability conditions, gave a geometric characterization of those quantum logics which are isomorphic to the projection lattice of a von Neumann algebra or aJ B W-algebra.

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Authors and Affiliations

  1. Department of Mathematics, University of Reading, RG6 2AX, Whiteknights, Reading, England

    L. J. Bunce & J. D. Maitland Wright

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  1. L. J. Bunce
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  2. J. D. Maitland Wright
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Communicated by H. Araki

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Bunce, L.J., Wright, J.D.M. Quantum logics and convex geometry. Commun.Math. Phys. 101, 87–96 (1985). https://doi.org/10.1007/BF01212357

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  • DOI: https://doi.org/10.1007/BF01212357

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