Abstract
We give an ortholattice theoretical version, bymeans of an ortholattice automorphism, of the theorem ofM. P. Soler characterizing Hilbert spaces byorthomodular spaces. Given an orthomodular space H and an orthoclosed subspace X of ℋ, we studythe group of all unitary operators on ℋ whoserestrictions to X and to X⊥ are bothidentical maps. This enables us to obtain completecharacterizations of the underlying division ring of a Hilbert lattice, for eachclassical case where this division ring is R,C, or H (the skew field of quaternions),by means of one or several ortholatticeautomorphisms.
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Mayet, R. Some Characterizations of the Underlying Division Ring of a Hilbert Lattice by Automorphisms. International Journal of Theoretical Physics 37, 109–114 (1998). https://doi.org/10.1023/A:1026669407606
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DOI: https://doi.org/10.1023/A:1026669407606