Abstract
The results about the isomorphism of a quantum logic ℒ with the logic of the projections in a separable Hilbert space previously obtained with the introduction of the topology of states are completed, including the case of non-separable Hilbert space, and showing that the continuity of the antiautomorphism ϑ of the division ring ℝ, ℂ or ℚ determined by ℒ follows from the general topological assumptions on ℒ.
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References
Cirelli, R. and Cotta-Ramusino, P. (1973). On the isomorphism of a ‘quantum logic’ with the logic of the projections in a Hilbert space.International Journal of Theoretical Physics Vol. 8, No. 1, p. 11.
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Cirelli, R., Cotta-Ramusino, P. & Novati, E. On the isomorphism of a quantum logic with the logic of the projections in a Hilbert space. II. Int J Theor Phys 11, 135–144 (1974). https://doi.org/10.1007/BF01811039
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DOI: https://doi.org/10.1007/BF01811039