Abstract
In this article I present some material of a forthcoming book with the titleQuantum Measures and Spaces. The main theme are generalizations of Gleason's theorem and spaces in which quantum measures exist. Characterizations of such spaces and classifications of their measures are given. The book will contain some supplementary results from the “orthomodular” theory under the heading “Miscellaneous.” It is a sequel to the bookMeasures and Hilbert Lattices of the same author.
Article PDF
Similar content being viewed by others
References
G. Kalmbach,Orthomodular Lattices (Academic Press, London, 1983).
G. Kalmbach,Measures and Hilbert Lattices (World Scientific, Singapore, 1986).
G. Kalmbach, “Quantum measure spaces,” partial Lecture Notes, University of Ulm.
H. Keller, “Ein nicht-klassischeer Hilbertscher Raum,”Math. Z. 172, 41–49 (1980).
H. Keller, “Measures on orthomodular vector space lattices,”Stud. Math. 88, 183–195 (1988).
H. Gensheimer, “Eine verbandstheoretische Charakterisierung von Hilberträumen,” Master's Thesis, University of Ulm, 1980.
H. Gross and U. Künzi, “On a class of orthomodular quadratic spaces,”L'Enseign. Math. 31, 187–212 (1985).
H. Gross,Quadratic Forms in Infinite-dimensional Vector Spaces (Birkhäuser, Basel, 1979).
H. Gross, “Different orthomodular orthocomplementations on a lattice,”Order 4, 79–92 (1987).
U. Künzi, “Orthomodulare Räume über bewerteten Körpern,” Ph.D. Thesis, University of Zürich, 1984.
A. Fässler-Ullmann, “On nonclassical Hilbert spaces,”Expo. Math. 3, 275–277 (1983).
B. H. Neumann, “On ordered division rings,”Trans. Am. Math. Soc. 66, 202–252 (1949).
P. Ribenboim, “Theorie des valuations” (Les Presses de l'Université de Montreal, 1965).
H. Keller, “Masstheorie auf orthomodularen Verbänden,” Lecture Notes, University of Zürich, 1988/1989.
A. Dvurecenskij, “Generalization of Maeda's theorem,”Int. J. Theor. Phys. 25, 1117–1124 (1986).
A. Dvurecenskij and L. Misik, “Gleason's theorem and completeness of inner product spaces,”Int. J. Theor. Phys. 27, 417–426 (1988).
S. Maeda, “Probability measures on projections in von Neumann algebras,” preprint,Reviews Math. Phys. 7, 235–290 (1990).
E. Christensen, “Measures on projections and physical states.”Comment. Math. Phys. 86, 529–538 (1982).
E. Christensen, Comment my paper “Measures on projections and physical states,” Preprint, 1985.
F. Yeadon, “Measures on projections inW*-algebras of type II1,”Bull. London Math. Soc. 15, 139–145 (1983).
F. Yeadon, “Finitely additive measures on projections in finiteW*-algebras,”Bull. London Math. Soc. 16, 145–150 (1984).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Kalmbach, G. Quantum measure spaces. Found Phys 20, 801–821 (1990). https://doi.org/10.1007/BF01889692
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01889692