On the Interpretation of the Lattice of Subspaces of the Hilbert Space as a Propositional Calculus
نویسنده
چکیده
G. BIRKHOFF and J . v . NEUMANN1 have shown in 1936 that the closed linear manifolds (subspaces) of the Hilbert space form a complete atomic and ortho-complemented lattice LQ which at least for finite dimensional subspaces is also modular. JAUCH 2 ' 3 , PIRON4 and KAMBER5 have pointed out, that instead of the modularity a weeker condition can be formulated in LQ which is always fulfilled for the lattice of subspaces of the Hilbert space, and which has been called week modularity2 or quasimodularity 5. A lattice LQ which is quasimodular will be denoted here by LQ.
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