Abstract
The paper On complemented lattices was the third paper in the new theory of orthomodular lattices which started in 1936 with Birkhoff and von Neumann’s idea of developing a new many-valued logic for quantum mechanics by using the lattice of closed subspaces C(H) of a Hilbert space H as the valuation lattice.
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References
G. Birkhoff and J. von Neumann, The logic of quantum mechanics, Ann. of Math. 37 (1936), 823–843.
R.P. Dilworth, On complemented lattices, Tôhoku Math. J. 47 (1940), 18–23. Reprinted in Chapter 2 of this volume.
K. Husimi, Studies on the foundations of quantum mechanics, I, Proc. Physics-Math. Soc. Japan 19 (1937), 766–789.
H. Gross and U.-M. Künzi, On the class of orthomodular spaces, L’Enseign. Math. 31 (1985), 187–212.
G. Kalmbach, “Orthomodular Lattices,” Academic Press, London, 1983.
G. Kalmbach, “Measures and Hilbert Lattices,” World Scientific, Singapore, 1986.
H.A. Keller, Ein nicht-klassischer Hilbertscher Raum, Math. Z. 172 (1980), 41–49.
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Kalmbach, G. (1990). On Orthomodular Lattices. In: Bogart, K.P., Freese, R., Kung, J.P.S. (eds) The Dilworth Theorems. Contemporary Mathematicians. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4899-3558-8_9
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DOI: https://doi.org/10.1007/978-1-4899-3558-8_9
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