Probability on Hilbert space effect algebras

Abstract

In [5] an important example of an effect algebra (in other terminology a D-poset, see [1, 2]) has been constructed  by linear positive operators on a Hilbert space. In the paper basic notions of probability theory are exposed and the central limit theorem is proved. Some similar results on D-lattices are known, but the effect algebra studied here need not be a lattice.