Hostname: page-component-586b7cd67f-vdxz6 Total loading time: 0 Render date: 2024-11-27T11:44:23.813Z Has data issue: false hasContentIssue false
  • English
  • Français

An elementary proof of Gleason's theorem

Published online by Cambridge University Press:  24 October 2008

Roger Cooke ,
Michael Keane  and
William Moran
Roger Cooke
Affiliation:
Department of Philosophy, Delft University of Technology
Michael Keane
Affiliation:
Department of Mathematics, Delft University of Technology
William Moran
Affiliation:
Department of Mathematics, University of Adelaide
Get access Rights & Permissions [Opens in a new window]

Abstract

Gleason's theorem characterizes the totally additive measures on the closed sub-spaces of a separable real or complex Hilbert space of dimension greater than two. This paper presents an elementary proof of Gleason's theorem which is accessible to undergraduates having completed a first course in real analysis.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 98 , Issue 1 , July 1985 , pp. 117 - 128
Copyright
Copyright © Cambridge Philosophical Society 1985

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

[1]Bell, J. S.. On the problem of hidden variables in quantum mechanics. Rev. Modern Phys. 38 (1966), 447–452.CrossRefGoogle Scholar
[2]Gleason, A. M.. Measures on the closed subspaces of a Hilbert Space. J. Math. Mech. 6 (1957), 885–893.Google Scholar
[3]Halmos, P. R.. Introduction to Hilbert Space (Chelsea, 1957).Google Scholar
[4]Kochen, S. and Specker, E. P.. The problem of hidden variables in quantum mechanics. J. Math. Mech. 17 (1967), 59–67.Google Scholar
[5]Mackey, G. W.. Mathematical Foundations of Quantum Mechanics (Addison-Wesley, 1963).Google Scholar
[6]Piron, C.. Foundations of Quantum Physics (Addison-Wesley, 1976).Google Scholar