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Some nearly Boolean orthomodular posets
Author(s):
Pavel
Pták
Journal:
Proc. Amer. Math. Soc.
126
(1998),
2039-2046.
MSC (1991):
Primary 28A60, 06C15, 81P10
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Abstract:
Let  be an orthomodular partially ordered set (``a quantum logic"). Let us say that  is nearly Boolean if  is set-representable and if every state on  is subadditive. We first discuss conditions under which a nearly Boolean OMP must be Boolean. Then we show that in general a nearly Boolean OMP does not have to be Boolean. Moreover, we prove that an arbitrary Boolean algebra may serve as the centre of a (non-Boolean) nearly Boolean OMP.
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Additional Information:
Pavel
Pták
Affiliation:
Czech Technical University, Faculty of Electrical Engineering, Department of Mathematics, 16627 Prague 6, Czech Republic
Email:
ptak@math.feld.cvut.cz
DOI:
10.1090/S0002-9939-98-04403-7
PII:
S 0002-9939(98)04403-7
Keywords:
Orthomodular partially ordered set,
Boolean algebra,
state (= finitely additive probability measure),
subadditivity
Received by editor(s):
December 16, 1996
Additional Notes:
The author acknowledges the support by the grant GA 201/96/0117 of the Czech Grant Agency.
Communicated by:
Palle E. T. Jorgensen
Copyright of article:
Copyright
1998,
American Mathematical Society
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