International Journal of Theoretical Physics

, Volume 37, Issue 1, pp 109–114

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

  • Authors
  • Rene Mayet

DOI: 10.1023/A:1026669407606

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.

Copyright information

© Plenum Publishing Corporation 1998