States and the free orthogonality monoid |
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Authors: | C H Randall D J Foulis |
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Affiliation: | (1) University of Massachusetts, USA |
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Abstract: | Let (X, #) be an orthogonality space such that the lattice C(X, #) of closed subsets of (X, #) is orthomodular and let ( , ) denote the free orthogonality monoid over (X, #). Let C0( , ) be the subset of C( , ), consisting of all closures of bounded orthogonal sets. We show that C0( , ) is a suborthomodular lattice of C( , ) and we provide a necessary and sufficient condition for C0( , ) to carry a full set of dispersion free states.The work of the second author on this paper was supported by National Science Foundation Grant GP-9005. |
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