Classes of conditional expectations over von Neumann algebras

Let N ⊂ M be von Neumann algebras and Eω: M → N an ω-conditional expectation mapping. For a state ψ of N an extension \gyEω of ψ with respect to Eω is described. The relation Eω ~ Eϑ defined to hold if \gyEω = \gyEϑ for every ψ is an equivalence relation. The family of equivalence classes possesses an affine structure and shows analogy with the normal state space of a von Neumann algebra.