Lattice theory,quadratic spaces,and quantum proposition systems |
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Authors: | Robert Piziak |
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Institution: | (1) Department of Mathematics, Baylor University, B.U. Box 7328, 76798-7328 Waco, Texas |
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Abstract: | A quadratic space is a generalization of a Hilbert space. The geometry of certain kinds of subspaces (closed, splitting, etc.) is approached from the purely lattice theoretic point of view. In particular, theorems of Mackey and Kaplansky are given purely lattice theoretic proofs. Under certain conditions, the lattice of closed elements is a quantum proposition system (i.e., a complete orthomodular atomistic lattice with the covering property). |
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