This is a preview of subscription content, log in via an institution to check access.
Literature Cited
G. Birkhoff and J. von Neumann, “The logic of quantum mechanics,“Ann. Math.,37, 833–843 (1936).
G. Mackey,The Mathematical Foundations of Quantum Mechanics, Benjamin, New York (1963).
V. VaradarajanGeometry of Quantum Theory, Van Nostrand, Princeton (1968).
A. M. Gleason, “Measures on the closed subspaces of a Hilbert space,”J. Ration. Mech. Anal.,6, 885–893 (1957).
M. S. Matveichuk, “A theorem on states in quantum logics,”Teor. i Mat. Fiz.,45, No. 2, 244–250 (1980); II,48, No. 2, 261–265 (1981).
E. Christensen, “Measures on projections and physical states,”Comm. Math. Phys.,86, 529–538 (1982).
J. Bunce and J. P. Wright, “Quantum measures and states on Jordan algebras,”Comm. Math. Phys.,98, 187–202 (1985).
F. Strocchi and A. S. Wightman, “Proof of the charge superselection rule in local relativistic quantum field theory,”J. Math. Phys.,15, No. 12, 2198–2225 (1974).
S. A. Malyugin, “On Gleason's theorem,”Izv. Vuzov. Matem., No. 8, 50–51 (1982).
Additional information
Kazan'. Translated fromSibirskii Matematicheskii Zhurnal, Vol. 32, No. 2, pp. 104–112, March–April, 1991.
Rights and permissions
About this article
Cite this article
Matveichuk, M.S. Measures on the quantum logic of subspaces of aJ-space. Sib Math J 32, 265–272 (1991). https://doi.org/10.1007/BF00972773
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF00972773