Orthomodularity in infinite dimensions; a theorem of M. Solèr

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.