We propose a representation r:L boolean OR Omega --> R-v, where L is the collection of closed subspaces of an n-dimensional real, complex, or quaternionic Hilbert space H or equivalently, the projection lattice of this Hilbert space, where Omega is the set of all states w:L --> [0, 1]. The value that w is an element of Omega takes in a is an element of L is given by the scalar product of the representative points (r(a) and r(w)). The representation r(a boolean OR b) of the join of two orthogonal elements a, b is an element of L is equal to r(a) + r(b). The convex closure of the representation of Sigma, the set of atoms of L, is equal to the representation of Omega. (C) 1998 Academic Press. [References: 18]
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