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Sasaki projections on orthocomplemented posets

Published online by Cambridge University Press:  17 April 2009

P.D. Finch
P.D. Finch
Affiliation:
Monash University, Clayton, Victoria.
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Abstract

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It is proved that an orthocomplemented poset P is an orthomodular lattice if and only if it admits a suitable defined set of order preserving maps. These maps are called projections. They are, in fact, Just the projections of the Baer *-semigroup associated with the orthomodular lattice.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 1 , Issue 3 , December 1969 , pp. 319 - 324
Copyright
Copyright © Australian Mathematical Society 1969

References

[1]Foulis, David J., “Baer *-semigroups”, Proc. Amer. Math. Soc. 11 (1960), 648–654.Google Scholar
[2]Foulis, David J., “A note on orthomodular lattices”, Portugal. Math. 21-(1962), 65–72.Google Scholar
[3]Mackey, George W., Mathematical foundations of quantum mechanics, (W.J. Benjamin, Inc., New York, 1963).Google Scholar
[4]Sasaki, Usa, “On orthocomplemented lattices satisfying the exchange axiom”, J. Sci. Hiroshima Univ., Ser. A 17 (1954), 293–302.Google Scholar