A constructive proof of Gleason's theorem (Q1283029)

Gleason's theorem states that any totally additive measure on the closed subspaces of a Hilbert space of dimension greater than two is given by a positive operator of trace class. \textit{R. Cooke}, \textit{M. Keane} and \textit{W. Moran} [Math. Proc. Camb. Philos. Soc. 98, 117-128 (1985; Zbl 0575.46051)] gave a proof that is elementary in the sense that unlike the original proof it doesn't appeal to the theory of representations of the orthogonal group. However, this elementary proof was nonconstructive. Therefore, the authors follow the general outline of Gleason's proof, modify some arguments of Cooke, Keane and Moran and give a constructive proof of Gleason's theorem.