Some Characterizations of the Underlying Division Ring of a Hilbert Lattice by Automorphisms
- Cite this article as:
- Mayet, R. International Journal of Theoretical Physics (1998) 37: 109. doi:10.1023/A:1026669407606
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.