A remark on Piron's paper

  • Ichiro Amemiya

    Hokkaido University, Sapporo, Japan
  • Huzihiro Araki

    Kyoto University, 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).

Cite this article

Ichiro Amemiya, Huzihiro Araki, A remark on Piron's paper. Publ. Res. Inst. Math. Sci. 2 (1966), no. 3, pp. 423–427

DOI 10.2977/PRIMS/1195195769