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Title: | On Gleason’s theorem without Gleason |
Authors: | Buhagiar, David Chetcuti, Emanuel Dvurecenskij, Anatolij |
Keywords: | Hilbert space Gleason measures Quantum logic Invariant subspaces |
Issue Date: | 2009-06 |
Publisher: | Springer US |
Citation: | Buhagiar, D., Chetcuti, E., & Dvurecenskij, A. (2009). On Gleason’s theorem without Gleason. Foundations of Physics, 39(6), 550-558. |
Abstract: | The original proof of Gleason’s Theorem is very complicated and therefore, any result that can be derived also without the use of Gleason’s Theorem is welcome both in mathematics and mathematical physics. In this paper we reprove some known results that had originally been proved by the use of Gleason’s Theorem, e.g. that on the quantum logic ℒ(H) of all closed subspaces of a Hilbert space H, dim H≥3, there is no finitely additive state whose range is countably infinite. In particular, if dim H=n, then on ℒ(H) there is a unique discrete state, namely m(A)=dim A/dim H, A∈ℒ(H). |
URI: | https://www.um.edu.mt/library/oar//handle/123456789/18422 |
Appears in Collections: | Scholarly Works - FacSciMat |
Files in This Item:
File | Description | Size | Format | |
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On Gleason’s Theorem without Gleason.pdf Restricted Access | On Gleason’s theorem without Gleason | 308.08 kB | Adobe PDF | View/Open Request a copy |
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