, Volume 37, Issue 1, pp 109-114

Some Characterizations of the Underlying Division Ring of a Hilbert Lattice by Automorphisms

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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.