Hostname: page-component-cd9895bd7-dzt6s Total loading time: 0 Render date: 2024-12-26T21:18:23.809Z Has data issue: false hasContentIssue false
  • English
  • Français

A Hilbert Lattice With a Small Automorphism Group

Published online by Cambridge University Press:  20 November 2018

Urs-Martin Künzi
Urs-Martin Künzi*
Affiliation:
Seminar Für Logik Universität, Bonn 5300 Bonn 1 W., Germany
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

We construct an orthomodular inner product space to answer the questions posed by R. P. Morash in his paper "Angle bisection and orthoautomorphisms in Hilbert lattices" [6]. For example we show that every automorphism of the Hilbert lattice belonging to our inner product space has the property, that no atom is orthogonal to its image.

Keywords

Primary 51D2515A63Secondary 10C05
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 30 , Issue 2 , 01 June 1987 , pp. 182 - 185
Copyright
Copyright © Canadian Mathematical Society 1987

References

1. Amemiya, I. and Araki, H., A remark on Piron's paper, Publ. Res. Inst. Math. Sci. Ser. A 12(1966/67), pp. 423–427.Google Scholar
2. Gross, H., Quadratic forms and Hilbert lattices, to appear in Contributions in General Algebra III, Teubner Publ., 1985.Google Scholar
3. Gross, H. and Künzi, U.M., On the class of orthomodular quadratic spaces, to appear in L'Enseignement Mathématique.Google Scholar
4. Orthomodulare Räume über bewerteten Körpern, Ph.D. Thesis Univ. of Zürich, 1984.Google Scholar
5. Maeda, F. and Maeda, S., Theory of symmetric lattices, Grundlehren der Math ., Springer, 1970.Google Scholar
6. Morash, R.P., Angle bisection and orthoautomorphisms in Hilbert lattices, Can. J. Math. XXV (1973), pp. 261–272.Google Scholar
7. Piron, C., Foundations of quantum physics, Benjamin Inc., London, 1973.Google Scholar
8. Ribenboim, P., Théorie des valuations, Les presses de l'Université de Montréal, 1965.Google Scholar
9. Saarimäki, M., Counterexamples to the algebraic closed graph theorem, J. London Math. Soc. 26(2) (1982), pp. 421–424.Google Scholar
10. Varadarajan, V.S., Geometry of quantum theory, Vol. 1, Van Nostrand, Princeton, 1968.Google Scholar