Quantum logics and convex geometry
It has been of considerable interest to characterize among quantum logics \((=complete\) orthomodular lattices) such ones being representable in terms of more familiar entities like the projection lattices of von Neumann algebras. Atomic lattices have been thoroughly investigated, while the authors previously succeeded in characterizing quantum logics representable as the projection lattices of von Neumann algebras or JBW- algebras subject to certain countability conditions [Commun. Math. Phys. 96, 345-348 (1984; Zbl 0586.03049)]. The main result of this paper is that a large class of quantum logics may be identified with lattices of projections arising naturally in certain convex sets, which enabled the authors to extend their earlier results.
scientific article; zbMATH DE number 3970747
scientific article