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Volume 2, Issue 3, 1966, pp. 423–427
DOI: 10.2977/prims/1195195769

A remark on Piron's paper

Ichiro Amemiya[1] and Huzihiro Araki[2]

(1) Department of Mathematics, Hokkaido University, 060-0810, SAPPORO, JAPAN
(2) Kyoto University, 606-8502, KYOTO, JAPAN

The following statement (Piron's Theorem 22) is proved: The lattice Z/(V) of all subspaces of a prehilbert space V is orthomodular if and only if V is complete (i. e. a Hilbert space).

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Amemiya I, Araki H. A remark on Piron's paper. Publ. Res. Inst. Math. Sci. 2 (1966), 423-427. doi: 10.2977/prims/1195195769