Piron's and Bell's Geometrical Lemmas (2001)
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by Mirko Navara
ftp://cmp.felk.cvut.cz/pub/cmp/articles/navara/geom_lem.ps.gz
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Abstract:
The famous Gleason's Theorem gives a characterization of measures on lattices of subspaces of Hilbert spaces. The attempts to simplify its proof lead to geometrical lemmas that possess also easy proofs of some consequences of Gleason's Theorem. We contribute to these results by solving two open problems formulated by Chevalier, Dvurecenskij and Svozil. Besides, our use of orthoideals provides a unied approach to nite and innite measures. 1
Citations
| 124 | On the Einstein-Podolsky-Rosen paradox – Bell - 1964 |
| 55 | Foundations of quantum physics – Piron - 1976 |
| 48 | Quantum logic – Svozil - 1998 |
| 46 | The problem of hidden variables in quantum mechanics – Kochen, Specker - 1967 |
| 43 | Measures on the closed subspaces of a Hilbert space – Gleason - 1957 |
| 8 | An elementary proof of Gleason's theorem – COOKE, KEANE, et al. - 1985 |
| 6 | Gleason's Theorem and Its Applications – Dvurecenskij - 1993 |
| 5 | On the problem of hidden variables in quantum theory – Bell - 1966 |
| 2 | Hidden variables and the two theorems of – Mermin - 1993 |
| 2 | In and Gleason's theorems and the logic of indeterminacy – Pitowsky - 1998 |
| 1 | K.: Piron's and Bell's Geometrical Lemmas and Gleason's Theorem – Chevalier, Dvurecenskij, et al. |
| 1 | A.N.: On the Gleason theorem for unbounded measures (in Russian). Izvestija vuzov 2 – Lugovaja, Sherstnev - 1980 |
