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Orthomodularity in infinite dimensions; a theorem of M. Solèr

Author: Samuel S. Holland
Journal: Bull. Amer. Math. Soc. 32 (1995), 205-234
MSC: Primary 06C15; Secondary 11E39, 16W99, 46C15, 51D99, 81P10
MathSciNet review: 1307904
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Abstract: Maria Pia Solèr has recently proved that an orthomodular form that has an infinite orthonormal sequence is real, complex, or quaternionic Hilbert space. This paper provides an exposition of her result, and describes its consequences for Baer $ {\ast}$-rings, infinite-dimensional projective geometries, orthomodular lattices, and Mackey's quantum logic.

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Keywords: Hermitian form, Baer $ ^{\ast}$-ring, projective geometry, orthomodular lattice, quantum logic
Article copyright: © Copyright 1995 American Mathematical Society

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