, Volume 37, Issue 1, pp 109-114

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

Purchase on Springer.com

$39.95 / €34.95 / £29.95*

Rent the article at a discount

Rent now

* Final gross prices may vary according to local VAT.

Get Access

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.