An extension of a characterization of the automorphisms of Hilbert space effect algebras
arXiv:math/0211016 · doi:10.1016/S0034-4877(03)90008-5
Abstract
The aim of this paper is to show that if an order preserving bijective transformation of the Hilbert space effect algebra also preserves the probability with respect to a fixed pair of mixed states, then it is an ortho-order automorphism. A similar result for the orthomodular lattice of all sharp effects (i.e., projections) is also presented.
12 pages, to appear in Rep. Math. Phys