Abstract
Two postulates concerning observables on a quantum logic are formulated. By Postulate 1 compatibility of observables is defined by the strong topology on the set of observables. Postulate 2 requires that the range of the sum of observables ought to be contained in the smallestC-closed sublogic generated by their ranges. It is shown that the Hilbert space logicL(H) satisfies the two postulates. A theorem on the connection between joint distributions of types 1 and 2 on the logic satisfying Postulate 2 is proved.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
S. P. Gudder,Pac. J. Math. 19, 81 (1966).
S. P. Gudder,J. Math. Mech. 18, 325 (1968).
A. Dvurečenskij and S. Pulmannová, On the sum of observables on quantum logics,Math. Slovaca, to be published.
V. S. Varadarajan,Geometry of Quantum Theory (van Nostrand, Princeton, 1968), Vol. 1.
S. Pulmannová and A. Dvurečenskij, Stochastic processes on quantum logics,Rep. Math. Phys., to be published.
F. Maeda and S. Maeda,Theory of Symmetric Lattices (Springer, Berlin, 1970).
J. Dixmier,Les algèbres d'opérateurs dans l'espace hilbertien (Gauthier-Villars, Paris, 1969).
S. Pulmannová,Found. Phys. 10 (1980).
A. Dvurečenskij and S. Pulmannová, Connection between joint distributions and compatibility,Rep. Math. Phys., to be published.
A. Dvurečenskij and S. Pulmannová, A note on joint distributions of observables, submitted toMath. Slovaca.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Pulmannová, S. On the observables on quantum logics. Found Phys 11, 127–136 (1981). https://doi.org/10.1007/BF00715201
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF00715201