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Abstract:We show that for any c-morphism phi from the lattice P(H) of closed subspaces of a complex Hilbert space H (dim H > 2) to another such P(H'), a conservation property for the angles holds: For every x, y in H, x different from zero and y different from zero, we have that the angle between x and y equals the angle between phi(x) and phi(y). This implies that every c-morphism is a m-morphism. Our proof uses Gleason's theorem; this result was suggested to us by the work of R. Wright.

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